why don't you implement Elasticsearch instead of mysql?
This is a widely used open source software. The most common setup for webhosters is still PHP / MySQL. Switching the database would make it impossible for a lot users to use it...
In addition, I don't think the main focus of Matomo isn't search (and especially full text search) where something like Elasticsearch would bring benefits.
marking this as a duplicate of https://github.com/matomo-org/matomo/issues/500 where we discuss alternatives. I doubt ElasticSearch be a real option though since there are faster / better alternatives that are also more SQL compatible