Quick, cheap, easy to administer and sufficiently reliable tests could be an opportunity to open up a bit more. However, what needs to come before them is a shift in thinking about the problem. Unfortunately, for now most countries prefer to simply keep their citizens away from all but the safest countries and keep citizens from all but the safest countries away from their own one. This largely explains why many countries are in no rush to review their blanket quarantine policies in favour of ones based on testing. They perfectly understand that replacing the quarantine with a test or even two tests will increase mobility - but that's simply not the goal. Quite the opposite, in fact. Which may be adequate only if the situation is considered to be a short-term one. For the long-term run, it's simply not sustainable.
For how long will this go on is yet to be found out. In the next couple of months we'll definitely see many more waves of tightening and relaxation of travel restrictions here and there. If there's a tested, safe and reliable vaccine in the coming months and mass distribution starts sometime in the first half of 2021, I see it as the immunity certificate replacing all other entry requirements. If not though, some other way round it will probably be looked into as you cannot keep the economy in hibernation mode forever.