If you don't do the first contact, you don't get the influence if it's a normal empire or an enclave. It's possible to get setups where you have lots of normal empires and enclaves you just came in contact with that you want to get that first contact stuff done for the influence.
Yes, they can change those bonuses, but that is actually easier said then done. Right now the things that give envoys are considered pretty good. If you make that pointless, you have then have to come up with something that continues to make those worth taking. Yes, some will still have the diplomatic weight bonus but the current one will only get you so far. Also IMO I find the envoy setup more interesting as a finite resource because it means having to make trade offs. Do you boost your clout in the GC or federation even more, but risk having the jerk neighbor be more keen on going to war with you? Do you pop an ambassador out of your federation to boost you GC clout so you can kill or help a bill. Do you pop one out of the GC or off of improve relations so that you can stop your federation's cohesion from tanking? There are a few other things you can do. Yes, most will probably just throw every envoy they have into the GC, but that doesn't remove the fact that we have some interesting decision making with the current finite envoy setup. I bring this up because I know the obvious solution people will suggest if increased envoys won't matter and let's be honest, you'll never have zero envoys kind of implies infinite number, would be to increase diplomatic weight or add it in the case of xenophile ethics. Yes, diplomatic weight is strong and useful, but it lacks interesting decision making choices and IMO that would make that route a step back overall.
I'm leaning towards we get finite envoys for what we currently have and first contact works off it's own thing because I'm pretty sure if the devs were going to scrap the current system, they'd come out and say it now. Maybe not give us the details, but given the lack of confirmation despite people asking, it seems like an overhaul of the current system isn't in the cards.