There are a couple of benefits associated with hosting and serving your own vector tiles:
There are no thresholds when uploading your own data to create the tiles.
You do not need external connectivity to use the tiles as the hosting can be done locally (i.e. you can work offline with the vector tiles).
There are numerous options if you want to host and serve your own vector tiles. The following GitHub repositories have comprehensive lists of the available options for vector tiles and those available specifically for MBTiles:
If you want to export an MBTiles file to a directory of files, you can use open-source tools such as Tippecanoe or MBUtil.