I assume that you're proposing that only the filters set by the map author would be available, presumably through a simplified menu system in the HTML5 export.
This is a good idea but a basic first step would be to beef up Power Filters and the improve the user interface - and I mean for map authors. The logic operands that Alf suggests should be incorporated and made available across all categories instead of just the basic "All or Any" options which apply only within groups such as markers, text, etc.
The interface for Conditional Formatting added in MM2018 would a good starting point. This is easy to use and while it doesn't contain a full range of logic operands or parenthesis grouping, at least the "All or Any" options can be applied across a disparate range of topic properties.
I suggest that Conditional Formatting should also be made available in HTML5 exported maps, alongside Power Filters. Again the map author would set up the formatting parameters and both these and any power filters would be available to the end user via a menu system.
Edit: I've also realised that when you export a filtered map to HTML5 it is displayed in its filtered state but with a warning a filter has been applied. If you click on this the filter is removed but unless I am missing something there doesn't seem to be any way you can return the map back to its filtered state.
This is undesirable on at least two fronts. For example, you might want to publish only the filtered version of the map to HTML5 but might not be aware that the full version is available only by toggling the filter switch.
On the other hand you might want to provide both the filtered and unfiltered versions of the map so the end user can switch between them but currently it seems you can go only from the filtered to the unfiltered view and not back the other way.
I will start a separate thread regarding this issue.