So - in my learning about mini-splits, they have very rudimentary filters, and like window units these are often mesh or screen which you wash with water. This makes a mini-split much less attractive to me as I would need to climb a ladder to get to the filter. I live in a dusty area, so this would be every 2-3 weeks. To ignore filter cleaning would quickly affect their efficiency and power use. And I would still need to run my HEPA filters.

Here is just one analysis I found, but most other unbiased reviews seem to agree:
https://aircondlounge.com/do-mini-splits-have-filters-to-clean-the-air/

We too have an old house (built in 1929), heated with a gas boiler and radiators so it is an enclosed system. A few years back, we had ducted A/C installed in the first floor and split units upstairs, and I can emphatically say it was the best home improvement decision we ever made. The central A/C filter doesn't get very dirty at all (no pets!), but the technician comes once a year and changes it as part of his cleaning routine. The split unit filters are quick and easy to remove and clean and we do that ourselves.

While we used the A/C more than usual this past summer, we generally use it only during heat waves since our night temperatures are cool. But in 2023 we experienced the effects of the Canadian wildfires, and being able to keep our windows closed 24/7 was a godsend; we never even had a whiff of smoke in our house.

Perhaps the split units wouldn't work as well if they were run for weeks on end, but here in upstate New York they are an excellent solution for dealing with shorter periods of heat or poor air quality. I would highly recommend them.