Not 100% sure (I may be wrong)
<nitpick> I think it was the double / that they said was a mistake. The protocol identifier is, however, probably important (http ftp safe etc.). </nitpick>
The questions here are interesting though, if we hack a browser then we can use safe:XX, however this means the browser perhaps can use http:XX as well, the mix though has to be agreed (i.e. safe with http, safe only etc.).
If we are to provide plugins to normal browsers then, AFAIK we cannot affect the protocol handler. Tor seems to also agree with this part AFAIK.
Of course it’s all code, so we can do anything, however a hacked browser like tor’s or even servo may be a way we can do anything, but maybe exclude those who do not want another browser (a big issue for many folks).
So then back to plugins and playing by the rules browser manufacturers stipulate 
My feeling is the browser should be integral to SAFE apps, where folk use their usual web browser for the web, but in safe apps the browser is a SAFE only browser. This does though draw a large battle line between safe web and clearnet web.
We also need to remember folk can and will create bridges between the two and it may take off as a simpler easier, but less secure network (in terms of browsing at least). This could be unfortunate but perhaps unavoidable.
So my feeling (right now) is that what folk know as a browser should not exist in SAFE, but SAFE apps should make use of a SAFE browser, maybe even looking very different from their web browser.
So Open Source win’s as usual, the best solution will win here, we just need to decide where our efforts go for now. With more resources we can have more options (bad for people to have too many options, the paradox of choice == stagnation and no choice).
Hmm, maybe I need to go into politics after reading this.
TL;DR My vote is a SAFE only browser that can easily be called from any SAFE app and never allows clearnet links. I know others will have equally compelling reasons not to restrict people like this and I know the only correct answer will be answered in the future looking back with the “obviously” statements 