I'm going to catch hell for this, but...
I wear a pair of boxers over my briefs, and I tuck my undershirt between them. This makes perfectly good sense to me for a number of reasons.
First, as the OP mentioned, tucking your undershirt under a layer of elastic helps prevent slippage and untucking. However, at the end of the day, I may untuck both my shirts, but I do not want the shirt which has been next to my ass all day to be exposed to the outside world. That seems unsanitary, even though my ass is generally clean. My method keeps the shirt away from the ass.
Second, at some point in your life, you might shart yourself. Now, this has not yet happened to me and may not have happened to you, but I read too many stories here on TexAgs about guys desparate to find a restroom after eating a chile rellano who end up messing themselves. If this was to ever happen to me, I could simply discard the briefs and still have underwear on.
Third, at any time, I can drop trou and do whatever I want, feeling secure that I will not accidentally expose myself to the world at large. Whether I am at my house or someone else's, I can remove my pants and be more comfortable but not obscene by just being in my underwear.
Also, my method reigns supreme in the arena of modesty. Boxers alone do not do a very good job of concealing potentially embarrasing random erections, while briefs and even boxer-briefs might be obscene in public because they tend to outline the moose nuckle, or in more technical terms, the cokhnballs. I can wake up in the morning and walk outside of my house to check the mail or get the newspaper, even with morning wood, and be completely decent to my neighbors.
There is really no downside to this novel idea, other than a tiny amount of additional laundry. It is not any hotter to wear, just like wearing an undershir with a tshirt is not excessively warm. I say to the OP and those of you who forcing your undershirt to coexist with your ass that you are missing out on the true freedoms that I experience.