Bitcoin will have problems with securing network way before all Bitcoins get mined. Most likely before mid of this century. How that will get tackle no one knows. Monero have great solution for it with tail emission that will kick in in 2023. So plenty of time for Bitcoin to see if Monero tail emission is bringing results and is also suitable for Bitcoin.
Most probably you have forgot about the TX fees.
In some assumptions, after ~100 years (or before the last bitcoin will be mined out), the total TX fees will be included into one block may sum-up into more than 50 BTC also (which is the original block reward). Then, why miners will go away and how bitcoin network will be unsecured ?
Yes, there will still be miners that works for transaction fee which would still generate some income however we don't know how much. This also begs the question that people who mine for bitcoin rewards are not going to stay (or at least not all of them will) when rewards are gone (it will never be technically "gone" but at least it will be very small reward) which means there will be less miners, which means slower confirmation times, and higher fee. Considering when the bitcoin reward is like this and we have problems of confirmation as it is, we really do need the lightning in order to not go crazy with fee prices and slow times.
In other perspective, there will be no possibility of mining out the last bitcoin or all 21 million bitcoins will be mined out in infinite time. Yes I mean, now one bitcoin is devised into 8 decimals and in future it may go 10 or 20 or even 100 decimal points also. It is possible with all electronic format thing.
When one satoshi is valuing one dollar then we will definitely need a new unit to divide 1 satoshi. This trend will continue until bitcoin finds a stable demand.
