For one-offs like obtaining an ID card, a one-time imposition of a bit more time might be reasonable. "We've installed fingerprint readers at every location where you can apply for an ID card but retina readers are more expensive so they are only available at the main government office" may be fine if you're referring to a passport issued every ten years. But requiring a fingerprint for a SIM card yet having no backup for that at point-of-sale is not.
This is the flaw in every single system designed by people who largely have no experience with people who have a difference in physical or mental characteristics than the designers. We see it in facial recognition trained primarily on people of a certain skin pigment. Social systems designed by people who are neurotypical. Transport systems implemented by people assuming a base level of technological or literacy skill. The list goes on.
The people doing the designing aren't being inherently mean or malicious, they're simply not thinking. And not thinking is very easy, but makes systems that are very impenetrable to people not included in that thinking.
Anything which is a non-standard fallback with limited use is likely to be less secure. Not because the method would be inherently worse, but just because reduced use means that less attention and effort goes into building and maintaining it.
To take a tech example, TLS downgrade attacks: you want to keep things working for older clients, but it’s possible for some party in the middle to intercept the traffic and feign non-support of the newer version (or stronger cipher suites), in order to push both parties to the older version or cipher suite, and if that older version or cipher suite has anything broken about it, now you have an easier target.
Applied here, if you allow a no-fingerprints route that’s less secure, be aware that attackers will devise ways of getting onto that path for their own malicious purposes. Perhaps they’ll forge a doctor’s certificate, perhaps use some kind of acid that temporarily removes their fingerprints, that kind of thing.
It’s an unfortunate balance. With TLS, you decide eventually at some point that the problems of still supporting the old, less-secure version are too serious, and so tough luck for people stuck on the old version. With this, I certainly hope it would err much more on the side of not locking people out of the System. (Fortunately, although this particular condition is very rare, there are a much larger number of people that have damaged fingerprints or fingerprints that don’t work in whatever readers get used.)