You're losing bitcoins means you've lost your bitcoin wallet. so if you can't recover that wallet, those bitcoins will be completely lost, it's impossible for anyone to recover it. and what miners can't recover by mining it somehow.  So the hope of lost bitcoins should be abandoned. Such is the concept of Bitcoin. This is how Bitcoin's algorithm works and no one can break this algorithm

It is possible but the community don't want it. They know that part of Bitcoin value is contributed by its limited supply, 21 million bitcoins.

They are smart enough to know that if in history, Bitcoin total supply can be voted by Bitcoin nodes, community members to increase its total supply, there will be more events like this to increase Bitcoin total supply many more times. Then, belief in Bitcoin and its fixed total supply will be broken.

This idea is only from people who don't have bitcoin and hesitate to buy bitcoins. They want to have more bitcoins in total supply to have cheaper price to buy. They are for their benefits, not for benefit of the whole community. They also miss a point that if Bitcoin total supply can be increased, they will not get benefit in a long term too.

How is the 21 million Bitcoin cap defined and enforced?
Can Bitcoin's Hard Cap of 21 Million Be Changed?

For people who are Bitcoiners and already joined Bitcoin community, it does not make sense to increase total supply.

For outsiders, who dislike Bitcoin or hesitated to join Bitcoin community, they want to see total supply increase with some reasons. One can be their hope to see cheaper price for 1 BTC to enter. Another reason is simply because they dislike Bitcoin and want to see its price to fall.

So as insiders, we have no reason to satisfy outsiders because of their benefits or just because they want to destroy Bitcoin value and price.

No, there is no way it can be fulfilled. Because your bitcoin is lost if you can recover then definitely try it. But it will never be possible for someone else to compensate you for this

If such a compensation system were in place, the value of Bitcoin would be much lower. Bitcoins have the highest value because lost bitcoins are not recovered.

Bitcoin model is the model of scarcity. If bitcoin is abundantly available for everyone, it will definitely lose its value. Even satoshi nakamato in the white pepper addressed this issue by saying that the lost bitcoins are advantage to the Bitcoin network because it increases it scarcity status. In his words, he is of the opinion that lost bitcoins should be regarded as bitcoin sent to everyone's addresses 
The bitcoin developers should and will not try to touch the 21 million fixed supply because that is the key to bitcoin success.

Yes that's right. lost bitcoins there is no compensation for those Bitcoins because the final supply of bitcoins will not increase. Whether you admit it or not, a lot of bitcoins were lost, especially in the early days of Bitcoin, so many people didn't realize that the value of bitcoin would be what it is today, so many of them forgot. Seed Phrases, theft, and transaction errors.

This is just an assumption as an example, if 5 million bitcoins can never be recovered again, then that would lower the maximum limit from 21 million to 16 million. So it is true as you said that the price of bitcoin will increase many times because the number of bitcoins is increasingly limited.

Correction, the maximum supply of Bitcoin will not decrease from 21 million to 16 million just because there are 5 million Bitcoins that was considered lost forever or that can never be recovered. Those 5 million Bitcoins will only be treated as less amount in the total circulating supply. The total supply will remain at 21 million and will not decrease due to the lost Bitcoins.

I believe the OP did not know the mechanism of operation of Bitcoin, that is the only reason why he can be asking that question. If the structure and the operating system are left as it is now and based on the initial plans, then nothing can be done as the OP wanted and your advice will be so correct in that regard. Well, all hope is not lost yet, we can only say that we can talk with the present mode of operation, but later in the future if Satoshi shows up again, maybe there can be some upgrades, addition and subtraction and unbelievable things that people did not believe is possible and also which people are clamouring now but for unheard.

Bitcoin is a project like never before and Satoshi had his plan though the plans are now known to be very faulty, and that is why projects like Ethereum are getting more relevance if not for the pioneer status of Bitcoin that is helping it. For now, we should enjoy it while it lasts and the Bitcoin you lost is lost forever since it is a decentralised system. No way such can be recovered, not even with Satoshi's intervention in this current Bitcoin system since it is an open-source, nothing is hidden.

This is technically true. Well according to price history f bitcoin, for every halving marker the price of Bitcoin creates a new floor price and makes the price higher. Talking about the lost BTCs, it wasn't proven yet that it was truly lost. It just happened that there is about 5 million BTCs that are not flowing. Which means it is not being transferred or circulated in the market. If the lost wallets and BTCs are proven to be right, then I would take that as a bullish sentiment because it just really decreases the limited amount of BTC to 16mil.

Lost coins are overall good for the market because the maximum supply is much lower and with lower supply and ever increasing demand it will eventually create this artificial scarcity that would raise the price of whatever is on demand which in this case is bitcoin, now that's the perspective of the whole market excluding the person that has lost those bitcoins. I don't even think chaos would even ensue, there's no way that you have been in this market for a long time and you still don't see how chaotic the market is? Bitcoin is a volatile asset that could just dump overnight without any reason or pump for the same thing, that's already chaos OP, no way that bitcoin could get more chaotic than that if you ask me.