"These bottom roots are functional up to and until the top roots are established"
How do you know this?
Your tomatoes have a tap root to perform all the functions of deep roots, in terms of uptake of water and nutrients; these surface roots are more for breathing, which I don't believe you'd argue is a task that can be fulfilled.
" I say that up to the time we pull the plant out of the ground the lower roots still have a function and are not useless, otherwise they would die and just leave the top roots to take over everything."
What makes you so sure that they don't?
Since it is not possible for tomato plants to naturally have that type of root at that depth, why would it have the facility to dispose of them? It is more likely to be feeding them.
Trench planting is a different matter; all the roots are at the depth they were meant for, and you may (eventually) benefit, but it will still cost you time at the start of the growing season.
The point is: deep-planting causes the plant, which is already leggy, to divert energy to root production, which can only take it from plant/tomato production. If it already has all the roots it needs, "Why waste the effort?"
Is it not the case that you are limited to two short growing seasons because of Texan summer heat?
Is it not the case that you need as many flowers ready for pollination as early as possible between when the night-time temperature is too cold to set fruit, and the daytime temperature is not too hot?
Are you not gasping for a real tomato by the time the season starts, and to bring that forward a week or so would be a godsend?
THEN DON'T PLANT DEEP.
Why do you think they never catch up? Just the stems? Why would that slow them down?