You forgot to say there is a cap in the maximum amount of PRE tokens you are able to get on a daily basis and that you cannot withdraw those until certain amount is held on your account, which is also not a wallet.

PreSearch is decentralized search engine

No. It is an old concept. It is a search engine which shows the result from other search engines. In order to get them you must visit their page, which is hosted in one location in the world. There is nothing decentralized there.