Yes, I understand you.
Shared hosting owners are trying to sell one physical server to thousands of clients at the same time; this is beneficial from a business point of view, but for this, all the inhabitants of this anthill must be small, quiet and inconspicuous. Therefore, sites on such hosting are subject to strict requirements regarding CPU load (usually questions arise when you spend more than 1% of CPU), the number and size of tables in the database, and so on. If you haven’t encountered these limitations yet, you will soon as your site grows.
It’s your right to choose the type of hosting, but if your site has already become large and you can afford a small VPS server with no restrictions, then I would recommend looking in this direction. They are very inexpensive this day.
Unfortunately, I cannot recommend to you other analogs of WPFTS that would perform fast searches through indexing and that would not use large index tables. This is the key thing, a quick search requires an index. And the index sometimes X times large than the source data.
You can also consider some solutions that store the search index on a separate dedicated server (Elastic Search cloud), but in this case you will also have to pay for an additional service plus upload your data to third-party servers, which is not always convenient.
If you have any questions, I’m ready to answer them.