The same as in other regulated professions. It would give the people on the front line who can see the consequences of the corner cutting an effective right to say "No, we're not doing this user hostile thing". This would be a significant barrier because it wouldn't be legal to ship software without the required professional approval and the professionals would be heavily incentivised not to sign off any corner cutting because they would be personally and professionally responsible for any adverse consequences if they did.

You glibly say "More schooling does not mean more trustworthy or careful doctors.". Yet the schooling and credentialing clearly cuts off huge numbers of would-be doctors who never pass the exams, never graduate med school, or never even get into med school, or decide it is too difficult in the first place. In the software realm, those people just go to some boot camp and they're off to the races...

Another huge aspect of credentialing is required ongoing education, which REQUIRES physicians and engineers to take updated continuing education just to maintain their license. This again continuously improves the talent pool.

And, if your main concern is that they be "more trustworthy or careful", credentialing also helps that by finding the worst, least trustworthy and careful and cancelling their license, so they are NOT doctors anymore. The untrustworthy or careless SWE just gets a new job to ruin stuff elsewhere, probably taking one from the actual good engineer because their talent is not engineering, but bullshitting.