Tap wrenches are designed like this one:
But with this design the bolt always untightens wile using the tool.
Why isn't it designed like this:
The biggest reason most tap handles look like your first picture and not like the second picture is pure and simple: control. The small ratchet head like you are showing in the second picture would not give the user any kind of stability as you try to turn it, mind you it might work okay for chasing threads, but definitely not good for trying to cut new one. Secondarily you have torque to consider. To cut new threads in steel or iron takes a good amount of torque. You couldn't even get 10% of the torque out of the smaller one than you can out of the larger T-handle you have shown.
As far as I know, the version you have shown is the most common for larger sized taps. You can see what is used for the smaller ones in the bottom right hand corner of this image.
Since this is a Snap-On set, you can imagine this is not "lower quality". You can also see it uses the same screw handle design as you showed in your picture. I understand your annoyance with them becoming loose, but would suggest two simple techniques to keep it tight during use. One, after every turn (or partial turn) tighten the handle. Two, keep tightening torque on the handle at all times while you're using it.
These are not perfect, but should serve you well to keep it from jumping off of the tap.
Just like sockets, taps come in a manner of different sizes.
However, if a standard size was used for the square end of the shaft it would limit the tap's insertability if too big, or risk over-torquing if too small. To avoid these potential issues, it is better to make the size of the square end conform to the diameter of the tap.
This explains why the tap wrench pictured is adjustable. What it doesn't explain is why the wrench loosens itself during use. I have a similar low-quality tap wrench and have found some success with a couple of techniques:
Of course, the better solution would be to get a tap wrench with higher build quality.