nobody likes their supply converging towards infinity
Your statement can be rephrased as "nobody likes their share of the pie to be decreased".
At first sight, that's seems obvious.
But on closer inspection, it's not so obvious.
For the pie to be useful, you want as many people as possible to have some share.
And you want this pie to be more attractive to people than some other pie.
So you don't want the pie ownership to be too concentrated. Maybe, if you believe in fairness,
you want future generations to have some share of the pie as well.
That's why you want the supply to keep growing. Preferably not by too much though. Just a percent or two per year.
That makes you not lose too much of your share while allowing many more people their fair share....
I've thought the same in the rather early days of Dogecoin: tail emission gives everybody the chance get hands of the coin, tail emission makes it much more suitable for being an actual currency since in every currency money lost do happen.
However, in those days Dogecoin price went down and no recovery seemed to be at the horizon (I never expected the 2021 comeback, but I still don't know if it was good or just manipulation).
Now I consider Dogecoin tail emission overly big.
Is tail emission good? Maybe, but it's overly difficult to get it right. Bitcoin is better as investment and only time will tell if its lack of tail emission is a real problem or not. For now we're okay and in the near future the existence of 8 digits after the decimal point can do the job. Then we (or actually one of the next generations) will see...