The carrots and potatoes need a longer roasting than the other vegetables. Also, roasting onion keeps it with a relatively "raw" flavor; if you want your onion to taste cooked and lose its sharpness, you should sweat it in oil on a stove before roasting in the case of eating the stuff roasted. If you are going to cook this stuff to a soup, don't roast the onion at all, just sweat it in the pot and then add the roasted vegetables to cook the soup.
Generally, roasting time for nonstarchy vegetables isn't that long. I would start with just the carrots and potatoes (carrots are not starchy, but they are woody and need a long time for the cell walls to break apart and soften; potatoes need some time roasting after the internal temperature has reached 70°C because of the starch). The garlic can also use a long roast, but I would cut it very fine and sweat it together with the onion. That depends on whether you prefer garlic-flavored oil infusing your soup or roasted cloves to bite on.
After the potatoes and carrots have been in the oven (tossed with a little oil) for 25-30 minutes (preferably covered, so they half cook, half roast in their own steam), I would add the tender vegetables (if you want to put the sweated onion in, that's the time for it too). Remove the cover to let the vegetables roast nicely. Then leave in the oven for another 25-30 minutes or until tender.
You won't get the strong roasted flavors of, say, a pepper roasted directly on a flame, but you will have some nicely cooked veggies. You can then cook them up for a very short time in a broth to make a soup (under a minute), or use them in other ways, for example as a side dish, or extending the recipe to become a casserole.
The two-step addition of the vegetables is important, because the tender vegetables like sweet peppers and zucchini become mushy when overcooked and dry when overroasted.
If you want to add spices, add them in the beginning, mixed with the oil. Dried herbs can also be added at the beginning, to have time to rehydrate a bit. Don't add fresh herbs at the beginning, they will wilt. Add them 3-4 min before the final dish (i.e. the soup) is ready.
What happens to bread when it is done
Yes, there is something particular what happens at a temperature in the mid-90s. Not all details of it are proven, but the major outline is, and the hypotheses about the details are solid enough to make it into textbooks.
Starch is contained in tiny granules, a few micrometers in diameter. When heated in the presence of water, there is a specific temperature at which these granules burst. The molecules of starch come in contact with water and the water molecules get lodged in the nooks and crannies of the much larger starch molecules. This process is called gelating.
You can observe it easily on the macro level. Just cook a bechamel or starch pudding on stovetop, stirring constantly. The liquid will stay rather thin until all will thicken at once, just before you see the first bubbles of boiling. This is when the starch gelates.
The same thing happens in bread too. This is why you want to heat the bread to this temperature. If you don't, you will have raw starch inside, which doesn't taste well.
The exact temperature at which this happens varies a bit with the type of starch. It is not the same for rice and wheat, for example, and I think that it is also a bit different between different wheat cultivars. But the range within this variation occurs is not so wide, all references I have seen move somewhere between 94 and 98 degrees Celsius. So the recipe author just picks a temperature he knows to work for the flour used in the bread, maybe also accounting for some additional heat transfer after taking out of the oven.
Can you use temperature as an indicator for doneness
The theory says yes. My personal experience also says yes. Why did you feel that your bread was too doughy? There are different reasons why this could have happened. You could have measured it wrong (with the probe being too close to the surface, where the temperature is higher). You could have cut it too early. (Bread is always doughy before the first starch retrogradation, which occurs maybe 1 hour after baking). It is also possible that the bread was actually done in the sense of gelled starch, but that the recipe produced a rather moist bread and that you have grown accustomed to dry breads if you normally bake your breads for a very long time, so your brain perceived the unaccustomed texture as "not right". Or it is possible that something went wrong with the leavening, making the bread too dense. Dense bread is always doughy, you cannot bake the moisture out of it.
technical criteria for bread doneness
There are two big chemical changes which happen to bread while baking. The proteins in bread (the gluten) have to harden. Before that, they are soft and pliable. At some temperature, they become rubber-like. The hardened gluten gives the bread structure.
The second change is the starch gelation I explained earlier. When this happens, the liquid part of the dough (dough consists of a liquid phase suspenede in the elastic gluten mesh) thickens. Gelated starch gives bread a fluffy, soft body.
As the starch gelates at much hicher temperatures than proteins denature, bread is taken out of the oven when the starch is done.
The third step is the starch retrogradation. In retrogradation, starch loses the water which it took during gelation. There are three big stages of it, after each the texture changes drastically. The first happens at about an hour after getting out of the oven. This is when the bread is considered done by textbooks. In practice, there are many people (including myself) who like the taste of the moist hot bread just out of the oven, and they consider it done at the previous step. The second happens after about 24 hours; after it, the bread is considered stale. The third step takes several days, and after it, bread is considered inedible, because it becomes hard as wood.
So technically, bread is considered done after it has been baked to gelation temperature and then left alone for 1 hour.
Best Answer
If after an hour they haven't softened up at all, and this occurs with different vegetables (so you're certainly not just encountering a batch of old, dried out gourds or something,) the problem is almost certainly an inaccurate oven thermostat. Oven thermostats are notoriously unreliable. Get an oven thermometer and see what temperature your oven really is.
for even cooking and optimal browning, you should arrange your vegetables in one layer on the tray. If this were the primary problem, the vegetables on either the top, bottom, and/or in the middle (depending on the intensity and direction of your heat source) would be undercooked while the more exposed parts would be more cooked.
Note, oil and water based liquids affect cooking very differently. Water-based liquids will get the vegetables to soften more quickly than oil because water transfers heat more efficiently than oil, and it can turn to steam which is a good medium for spreading heat evenly on an uneven surface (such as a pile of chopped vegetables.) It also kills any possibility of browning because water doesn't get hotter than 212. Just because it's in the oven, it doesn't mean you aren't steaming your vegetables rather than roasting them. There's nothing wrong with steamed veg, but that's a very different end-product than roasted veg. More oil will create more crispiness, but a thin, even coating over all of the vegetables should be the only thing you need to roast them properly.
Now, about that recipe: 175 is low for roasting those types of vegetables. Even without par-boiling/steaming them (which lets you finish them at a higher temperature for more even browning and crispiness,) I'd still go with something around 220. That said, even if the cut vegetables were heavily refrigerated, you still shouldn't be waiting hours for them to soften up if your oven was actually 175. Get an oven thermometer!
Good luck, and happy roasting!