Wouldn't it be better if lost coins were reintroduced into the network after a fixed span of inactivity?
Reintroduced by whom? Individuals control the private keys to their BTC, so if any lost BTC is going to be reintroduced, it has to be if the owner finds the private keys to their funds. It is not even possible to be sure of how much BTC's are lost, because it does not mean funds are lost if it has not moved from an address for many years.
I suppose the first thing one would say no for, would be by virtue of bitcoin's acclaimed deflationary property. This said, I believe it is much more important, especially in the longest term, that bitcoin keeps its property of conservation of energy, that is, having a fixed quantity of money ever available. By losing coins, instead, and by having them unrecoverable, we have not a fixed quantity of money, rather a decreasing one, which is why we call bitcoin deflationary.
Lost BTC's do not increase the number of BTC's in circulation, it reduces it, only 21 million BTC's are going to be mined, if you add the ones that are lost, then a few million less would be in circulation, but not more than the capped 21 million, and this doesn't affect the BTC network any bit, it should even make BTC more scarce and more valuable.
What would happen if we would make so that coins with 109 years of inactivity would be reintroduced into the network?
BTC was created only 14 years ago, and only the owner of a private key can move their BTC no matter how long it has remained inactive in an address.