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QR codes were created for labelling automotive parts, not for URLs. Part numbers are usually uppercase alphanumeric, with a few punctuation characters.

QR codes existed for over a decade before smartphones brought them into the mainstream. They're high density replacements for barcodes, which are uppercase by convention (or in some cases like Code 39, only support uppercase). URLs in QR codes are a later innovation.

Urls can include parameters and for those capitalization can definitely matter.

domain name and protocol name is case-insensitive.

If you care about QR code size, you should use URL shortener service which you can program in whatever way you need.

So I don't think that's major restriction.

Then your qr code only works if the url shortener stays online.

In many cases its wiser to roll your own permanent shortened urls so you aren't beholden to a third party service.

Of course you can roll out your own URL shortener. It's not a problem to buy short domain.