You're not wasting the speed of the scout in arena. Running into a group of 12 people is pretty much guaranteed death.
Scout in arena is exactly as you're doing. You need to wait for people to spread out and rely on your teammates audio cues and voice communications to know where to go. Listen for sniper calls or watch the death tracker for sniper kills and then go pick them off. Pick off stragglers who might be retreating to find health after a larger fight. Arena means that every death is a tip in balance, and as you're the MOST fragile player, you've got a lot of liability on your shoulders to ensure that you don't waste your life right off the bat (no pun intended). Use your double jump to your advantage and consider using the FaN to get to good ambush / hiding spots.
Scout in arena can also be effective bait. Get that demo to chase you around the corner into the hands of a heavy/medic combo. A lot of people will tunnel vision and auto target scouts due to their low health.
To put it simply, if you're playing scout in arena, you're playing more like a spy in any other match.
Edit: Adding in a bit about defensive play.
You can also treat scout in arena like a 6v6 competitive match as the defensive scout. Your job is to protect the medic who will likely be glued to a soldier or heavy early on. If the offensive target (heavy or soldier) is an attentive player, the FaN is a great choice for this due to it's stopping power, buying them a few seconds to turn and destroy (assuming they're not dead already). If they're not terribly attentive, your normal scattergun will do the trick and you're just going to be trying to kill and dodge.
Lastly, while I don't use it often (I love me some pistol action), you can use the Bonk! Energy Drink and park yourself between the medic and his assailant to effectively create a wall for 6 seconds while the heavy / soldier / whatever has time to refocus and destroy them.
Moral of the story: Medics can win arenas. Treat them well.
In addition to learning the maps, there are a few other things to know:
- Sentry guns beep 1-3 times each time they change directions (so about every 3 seconds). Once for mini/level 1, twice for level 2, thrice for level 3. Generally, if you can hear a sentry's beep, you'll be in its range when you round a corner.
- As a Spy, you'll get a LOT of cheap deaths. Sadly, this is because of the Spy's shortcomings in order to combat the instant-kill backstab.
- The Spy's Dead Ringer takes some getting used to, but in certain situations, using it (preferably while disguised as a teammate so they don't know you're a Spy) can get past a defensive line. Beware that the Dead Ringer makes a louder than usual decloak sound. The Dead Ringer is a "perfect" cloak for the first 6.5 seconds, so enemies who touch you won't make you appear as a team-color outline. However, they still can't move through you.
- The Cloak and Dagger gives you some latitude by not decloaking when you don't want to, but it also has a very short cloak time.
Having said all this, you're still going to die a lot in Team Fortress 2. It's the nature of the game! The lower-HP classes in particular are specialized in some way, but lower HP is the drawback.
Best Answer
Scout is a class with a very high skill threshhold to clear - playing Scout and doing it well is very difficult, especially for a new player. They move faster than any other class, making it more difficult to aim properly. And they have the lowest possible base HP of any class (unmodified by loadouts).
Mobility is key to playing a Scout. You never want to be in one place for long. Jump, weave, and duck into side-corridors to get away from danger.
You are vulnerable, and you do not want to get into a head-on fight, even against weaker classes. Instead, use side-corridors to flank and get behind other players.
Your Scattergun (and the FaN if you have it) are powerful close-range weapons. Don't shoot until you're up close and certain of getting a full-body shot. The more pellets you can get into them in a single shot, the greater damage you'll do.
You can take down most classes in just two shots at close range, which is faster than most classes will be able to react. If they do, dodge, and if they are well aware of your presence, run. You are outgunned by almost every class that isn't support-based.
Avoid sentries. Always, always avoid sentries. Use Bonk! to get past them, pick them off with a pistol, slip by them if they aren't pointing directly at your pathway, but avoid them at all costs.
Finally, above all else, practice. Every class has a skill threshhold you need to get past before you're 'good' with them, and the Scout's the hardest class of all to get used to. Watch some video clips, watch what other players do, read the TF2 Wiki pages on Scout Strategy and match-ups, but practice above all else makes perfect.