Singapore is developed enough to give free public wifi, some location even surpassing 200mbps, far more than the mentioned 5mbps.
I am sure they can easily just give every Singaporean a free permanent 'premium' phone number which would solve all the issue mentioned above.
Since NRIC is no longer sensitive data, just tie it to NRIC to prevent abuse, we still have plenty of unused prefix like 2,4,5,7.
Assuming Singapore phone number system isn't stuck with just 8 digit, which it shouldn't be due to "14.6" of the National Numbering Plan.
If someone NRIC is S1234567D, then their personal permanent phone number can be xy1234567, where x is one of the unused prefix and y is another digit for [S,F,T,G] grouping.
The 'base' plan can just be no data, no outgoing call/sms, incoming get charge to caller/sender like when using premium number, and of course usable with singapore free public wifi (wireless@sg).
I would have no reason not to answer calls from private number or anyone else then if they are the one being charged.
It can be given out as an esim via the singpass app, physical sim can be requested/distributed via digital clinic.
As for the no sim = no wireless@sgx = no internet to register issue, there are plenty of other free wifi option if people require internet access for first registration like Malls, McDonald/BurgerKing Wifi, Decathlon etc.
'data and outgoing' add-on, to be consider further down the line, can be provided by existing telecom, when add-on expires, it fall back to the 'base' plan (kind of like SP with electricity).
Nobody will be required to get this number, attempting to call an unregistered number will just get the standard answer (ie: the end/drop call tone), so people with famous NRIC can just choose not to register for their number.