Why wouldn’t you just put small taps without the recess in a T handle which does have the recess.
-I'm not the last word on much of anything, all I do is offer my experience, a few reference books, and my opinion. Not everybody has the T-handle type, I don't care that much for them and use mine only when reach is an issue. I much prefer the straight type tap handles as they give me better direct feedback from the tap as to how it's doing. When a tap is somewhat dull or the material is just tough (work hardening) I can "feel" whether the tap is actually cutting or just pushing material. When that happens there's a good chance of it breaking and making a simple task a larger PITA. Even when the tap is cutting ok the flutes can get clogged up with chips, new chips will have nowhere to go and the tap starts to bind up. That's where feedback is important to me. I know, by feel, how a tap is doing and whether I need to back it out of the hole or not. I've had several instances where I needed 3 brand new taps to create ONE threaded hole. Even with power tapping I'll often just get the tap started to ensure it's aligned with the hole axis and then finish it by hand. I'll power tap when I feel confident about the outcome but even aluminum, as soft as it is, can create a situation that breaks a tap. I really hate digging a broken tap out of a hole just because I got in a hurry and failed to consider the conditions. That's sorta like the "too fast for conditions" traffic infraction. Taps over 7/16" are usually a fairly safe bet for power tapping.
No "chamfer" on the end of smaller taps is likely because it would be more difficult to do with the smaller sizes although I may be wrong about that. I never really considered the "why" because I felt it it didn't need one anyway. JMO. Hope this helps someone.