In the refuelling era in 90s, the disadvantage of heavier fuel low after pit stop usually "out-weight" the advantage of new tires, this encouraged drivers to just passively sit and wait . However the current tire undercut more likely to encourage drivers to offensively push a faster laptime / strategy thus more exciting race for the viewers.
Not really. Previously they would sit and wait for the car ahead to run out of fuel and pit. Now they sit and wait until the field spread is sufficient to make the undercut worth it. In both cases, you get fast laps around the stops.
There's no way of forcing all cars to push all the time. If you made overtaking significantly easier, you'd take away the incentive to sit behind people and wait for an opportunity to do something around the stops, but then the cars would end up, within a few laps, in race pace order at which point the ones with the most pace would not push as hard. They would only push hard enough to maintain their gap to the car behind.
I don't understand what the problem is. It's a race, not a time trial. You get the same number of points for winning by a small margin as you do for winning by a large margin. You can't force people to push harder than what is in their interests.
Also, drivers have to balance conservation of brakes, fuel, tyres etc against pace. There's a skill in that. Most of the exciting racing at the end of stints, or at the end of the race, comes about because one car/driver has fresher tyres and, possibly, more fuel than the car ahead and is therefore able to attack. If you make people run the same fuel load, that will happen a bit less, particularly at tracks where they don't need the full race allowance. All things being equal, these cars can't pass each other even if they have a lot more pace than the car ahead. It will be better to sit there and take whatever points are on offer than to make a futile attempt to get past.