Yes but those are near lifetime immunities. Not said (that I'm aware of) with these two covid vaccines is how long they protect for. If it is less than a year it will be very hard to get and keep people taking it.
The cost of getting a booster every year is minuscule compared to the number of lives lost, not to mention the hit to the world economy.
A working vaccine is a huge W. If immunity only lasts 12 months instead of 10 years that just decreases the font size down to 64 point from 72 point. I'll take it.
The 5 year immunity level is not knowable.
Which is why monopolies are bad. You don't have a pack anymore, and the leader(s) don't have incentive to do much disruption.