IMO that's the problem of the screen reader/search engine. It's a fine line between "accessibility" and actively making things worse (i.e. less accessible) for the majority just to cater to a small group of screen reader users.

That's similar to replacing all major doors in a building with automatic ones that can't be operated manually and take forever to open, despite the typical occupancy by wheelchair users being 0. Accessibility is great, but accessibility for few should not come at the cost of accessibility for most.