I've seen the 300gr .338" A-tip punch right through at 150 yards (still killed the deer), but came apart and balanced out very well at 600 yards. Starting mass makes a huge difference with lead core bullets just like it can and does with monos. Sometimes mass can be too high and the expansion is delayed to the point it's already exited by the time it could really open up. As velocity lowers, the expansion timing is better. Amount of resistance upon impact makes a big difference too. In that example, a more substantial animal would likely have allowed that bullet to expand well even at 150 yards.
I've killed a lot with a 208gr ELDM (AMAX prior to it) and 195gr TMK too at pretty high impact velocities and they've always performed beautifully. I've used many other lead cores, but those two significantly the most, as far as a version of soft construction that many would think would just blow up on or near the surface. They never have.
Bullets like that don't "over mushroom". They shed material as they mushroom and that allows them to keep penetrating until they either exit or do indeed lose enough momentum to stop. If there's insufficient starting mass, or too much with too little resistance, they tend to perform more unfavorably. Monos with too little or too much mass tend to have their own complications from that as well.
And yes, the trend continues to be high BC. Hornady is pushing towards to more now, but others like Berger have for a while. Sierra too with the TMK and TGK. The Raptor, Lazer, and MTH from Cutting Edge has pushed BC for a long time as well. I do not foresee this trend going away either. Hunters and shooters will continue to demand more and better and the manufacturers will continue to try to give themselves the edge over their competitors.