My preliminary views are as follows:
To avoid all these controversies, ideally, exemption should have been withdrawn and RCM liability should have been imposed 'where the residential dwelling is rented to a registered person in course of or furtherance of business of such registered person'.
On plain reading of recent amendments, your observations are right that such proprietor is liable to pay GST under RCM on residential dwelling taken by him for personal use AND he will not be entitled to avail ITC there-against.
This is so because proprietorship firm and proprietor is generally treated as one and same thing.
However, if such interpretation is indeed taken, such levy - in situation under discussion here - may be held as unconstitutional being discriminatory (between registered person and unregistered person, without any intelligent criteria / reason for such discrimination), tax on business or profession and so on.....
Such levy, if upheld, is essentially an additional burden (@18% of rent) on a proprietorship entrepreneur - who has to taken GST registration & contributing to state and Centre exchanger - just because he also needs to take residential dwelling on rent for personal use.
Any way, it is indeed need of the hour if Govt. comes with suitable clarification and amendment/s to avoid such burden upon hapless proprietor for getting residential dwelling for personal use.
These are strictly preliminary views of mine and the same should not be construed as professional advice / suggestion.