Very soon people would not only die from rare bacteria related decease but any kind of random bacteria infection.
The only remotely viable solution is improving access to ERs.
If you don't consent to the rules, that is fine, you aren't allowed the drugs at home (same as today).
Telemedicine plus improving 24-hour pharmacy distribution and equipping them for rapid door-to-door delivery of critical meds (possibly by drone) might work, and might soon be more viable than ERs for the particular use case.
ER access addresses a lot more problems and probably wins aggregate cost/benefit analysis for the foreseeable future.
Of course I'd do whatever it took to save myself or my loved ones. Anyone would. That's not a good basis for government policy.
(Also, being honest, the number of situations where powerful antibiotics now vs. at the hospital would make a difference and the people involve realize that and administer them has got to be tiny. We can't make policy based on low-probability hypotheticals.)
It might save hundreds and but also kill thousands in the short-term, too: powerful broad spectrum antibiotics aren't without adverse effects, perhaps especially if taken in a genuine emergency that just isn't the kind of emergency the user thinks it is.
A single guy having strict antibiotics discipline doesn't mean anything when you have 1 billion+ countries like India where strong generic antibiotics are sold to anybody over the counter (at least that was the case in 2010).
Once I didn't have them on Kilimanjaro and I went from being perfectly OK to almost passing out within 1 freakin' hour from extremely strong gastro infection. Luckily peace corps members of the team had some and they almost immediately helped a lot (I still had what one can call a shitty experience of the peak, albeit successful). In situations like these you don't care about long-term good of the mankind, you just want to survive, far from any professional help.