This is also true, but this problem predates this season - we've had trouble breaking through pressing teams for close to the entirety of the time pressing has been a thing in the Premier League.
I'm not joking - we have always struggled against the press to varying degrees, even under Poch when we were the arch-pressers ourselves. I remember his first game against Klopp as an example of this - Poch's first game against Pep had seen us beat them utterly hollow on the way to a 2-0 victory that should really have been 5-0, with us hunting down and dispossessing City's panicked players at will.
But when we played against Klopp, who had only arrived a week earlier, his team counterpressed us ferociously, and we actually struggled to get out of our half. We scraped a 0-0 that day, iirc.
In the early years, when we were the pioneers of all-aspect pressing, we had a trump card when counterpressed that hid our weaknesses as a unit - Dembele, who truly was a once in a generation player. He allowed us to press, and made it *very* difficult to counterpress us. But outside of him, a lot of our players struggled under the press - even our attacking quartet of Eriksen, Alli, Son and Kane. And as Dembele declined, our ability to play out of the press declined with it, until 2018/2019 when our approach was bypassing our midfield entirely and just lumping it to our forwards, because we couldn't hold it in midfield at all. Somehow, our fitness and the quality of our forwards in Kane, Son and Eriksen scraped us into the CL final, but it was clear we needed a change.
Accordingly, following 2018/2019, we signed Lo Celso and Ndombele to add to Alli, precisely because, on paper, they would comprise the most all-aspect pressing and press-resistant midfield in Europe. Sadly, one was a permacrock, one was a fat waste of space, and one had lost everything that once made him a good player - and, with our last bits of technical skill in midfield gone, we regressed to being a low block team, encouraged by the caveman-like approach of Mourinho who took away the one thing that had allowed us to compete despite our declining technical levels - our fitness.
So, there's a point to this story I'm telling - it's that, although we introduced the high-press to the league (well, after Soton, anyway), we were never good at evading it ourselves. Other teams were - they got better at it, they built teams full of players who could play through the press, from goalkeeper to striker. Liverpool and City most prominently.
To get back to the levels of dominance we enjoyed in 2016/2017, we can no longer rely on having a unique one-off player like Dembele to save us - we need to become press-resistant, and it needs to be right through the side.
We cannot replace Kane and Son, although neither of them are...great at evading the press. But we have to replace Dier, and we have to replace Davies, imo.
Now, whether we can actually do that is open to question - as you said, not many good players around in either position atm. But we have to do it if we really want to get anywhere, imo - otherwise we will always look limited against technically skilled teams like Chelsea, whenever we come up against them.
