It's NOT blackmail, she just likes to tease, and he likes to grumble but goes along with it
The prejudice/moaning about 'dem Gyarus is an excuse plot device that gives MC license to friendzone and be in denial about his attraction, grumble for comic effect, and be effeminately patriarchal and judgy without it being all creepy
The Freeloader vs. Shameless Exploiter of Freeloader dynamic makes it balance and work without making either side leave too much of a negative impression... manga doesn't dwell on it much, but the guy doesn't seem to have ANY money, and she appears to be fully supporting him --- wouldn't really sit well with his macho lecturing if she WASN'T slavedriving the hell out of him, as well as vice versa
And of course that sets the stage for HouseHusbandry 101 pigsty cleaning tips, the "subliminal message" lecture behind this series
...all in all, it balances out and works. Sympathetic cast, oddball non-traditional living arrangement, immodest girl gags, housekeeping tips