When thawing meat in cold water, why must one change the water regularly

The difference between cold and frozen where a refrigerator is concerned is actually only a few Kelvin (or "degrees").

The standard refrigerator will have warmer and colder zones, typically the top shelf being warmer, the bottom shelf above the veggie drawer cooler. Likewise the back is usually cooler than the front. The temperature you set it to is an average value. (Check your manual for your model.) In mine, anything on the back of the lowest shelf can, on occasion, be slightly frozen, but I have set it to 4 C.

Also, thermostats in kitchen appliences can easily be off by a few degrees. We have discussed this for ovens here on the site often enough, the same is true for fridges and freezers. A calibrated thermometer can tell you more.

So once you have made sure that your meat actually can thaw by putting it on the top shelf and adjusting the temperature setting, it's all about patience. The time it takes for a piece of meat varies greatly and for a big "lump" like a whole roast, defrosting overnight won't happen. Prominent example: Around Thanksgiving the defrosting times for turkey are discussed all over the web and plenty of anecdotes told about cooks forgetting that it may take days for a large bird...

That's one of the reasons why it's generally recommended to freeze food in smaller, especially flatter packages where possible (e.g. steak or chicken breasts side by side, not on top of each other): It freezes faster (-> food safety) and thaws faster (-> convenience).

Cooking meat while it's a little frozen generally works fine with methods that have some wiggle room in how much extra time you can add. Unfortunately this isn't the case with frying, and even if you cut the meat into small pieces I don't think you'd have much success.

My favorite method to quickly thaw meat is using a microwave. Most microwaves have a thaw setting, and it's often based on the weight you select. Typically microwave thawing is just done on a very low power, but you need to be very careful and frequently check/turn the meat or it may start to cook. This page has a really useful guide on thawing methods.