Infinite/grippy tyres will reduce the overtaking even more. You can't pass someone doing 200mph around a 90-degree bend if your car can do 200.05mph, which is the sort of margins we're getting down to these days.
The truth seems to be that the cars are a lot closer these days than before, for more of the race than before. By close, I mean in terms of lap time potential they are all within 107% comfortably and during the race they are pretty consistent. The steep tyre deg curve was supposed to mean that you could either go fast and "fall off" or drive more tentatively and go longer. Over a "stint", the sums are pretty simple - you might gain 0.2-0.5s a lap over 10 laps (2-5s advantage) but fall short of the end of the race forcing an additional stop which might lose you 15+ seconds. The conclusion is obvious! If you can make your tyres last an additional few laps and that is enough to offset an extra stop then it is the fastest way, even if the cars can go faster outright. The aim of the race is not to set the fastest lap, it is to finish the race distance as fast as possible and driving flat out is not necessarily the solution to that. These target loads lead to target lap times and the teams target lap times won't be too dissimilar, so there's no real incentive to actually overtake unless the aero loss of following is pushing your tyres out of the window. You don't get massive deltas between teams because they are all too similar for that to be the case now. You no longer get the sort of low speed masters vs high speed masters car builds now, they are virtually identical.
This will exist no matter what the compounds available - introduce super super sticky rubber that lasts the entire race? Fine, it will become a procession as they all manage their fuel. Introduce refuelling? Fine, it will become a procession as they all manage engine wear. Remove the engine limit? Fine, it will become a race to spend as much as possible on one-shot engines again and the sport will disintegrate.
IMO, the solution isn't chasing the minutiae of detail around tyre compounds and how much fuel should be allowed and so on. The solution is a cost cap that is high enough for the top teams to feel they can extract value from being in the sport but low enough that junior teams can enter. This cost cap would cover the entire team's operating budget and so with the right amount of advertising revenue could mean the teams were actually profitable or at least sustainable/viable as a business rather than a massive PR exercise. Create some sort of incentive structure for the constructors to gain a competitive advantage the less they spend - maybe a Constructors point or two for every £1m they are under the cap or something. Then couple that with removal of all non-safety critical technical regulation bar some overall dimension limitations. Lets see what the engineers can really do within a framework that encourages ingenuity but also rewards being thrifty.
We'd once again see nutcase cars with 6 wheels and fans sticking them to the tarmac and that might just actually be exciting!