Pavel wrote Pttp in the late 90's. This article was written in what, 2012? 2013? The man is allowed to change his mind on some things. Furthermore, he doesn't say that he no longer likes side press, bent press, etc (bent press is still taught in SFG2, one arm and two arm kettle bell press in SFG), just that maybe they are not the best overall choice for everyone. In addition, a while back on the dragondoor forum, he said that if he would re-write pttp, he would change it to bench press because almost no one followed his advice to do the side press anyway.
Here's some thoughts of mine on the subject. Other than a several week period where I followed Pavel's bench to military press more article, I've never benched. I got my start with weights with pttp, then etk, and have always put things overhead in a variety of ways. However, if I had it to do over, I might very well consider it, and have experimented a bit in using it with some people for pttp. While it can be a very technical movement, especially in the hands of a geared powerlifter, it can also be learned fairly easily at a low, basic level, which I have not really found to be as true with the barbell side press, especially for beginners. Progress is also easier. I have also heard it said, although I don't have the experience to verify, that bench supports overhead presses better than the other way around. So it might not be bad to build some strength there first. Certainly, in the days of the press as a competitive lift, many great olympic pressers, including Tommy Kono, used bench and or incline bench as an assistance exercise, so it must have some carryover.
Bench, when done properly, and over time, becomes a whole body exercise, and if one is not going to the outer reaches of powerlifting competition, it is by no means inevitable that injuries will result. I have many counter-examples and this was discussed on this forum and others a while ago.
Bent press is also an excellent exercise, and can be a good standalone press, but it's not suitable for everyone's needs and circumstances and abilities, although I do think it should get more attention than it's been given. I think the barbell press has also been unfairly overlooked, and think it goes well with pttp; I've been using it that way recently, with good results. Lastly, I think for many reasons, including practical ones, the side press and bent press are better done with a kettlebell for most people, like the getup (which can also be done with a barbell), so they fit better in that framework.