Concur with most of what's been written re intended to prevent lateral movement, but are more of a marketing/showoff ploy.
The ones I've seen tend to have been on pigeon and 'fowling guns - guns built to throw heavier charges which may loosen a gun sooner - but I did handle a wonderful pair of Woodward "automatic" patent game guns c1888 some weeks ago which were sideclipped (incidentally: this pair are the kind of fabled guns we don't get to hear much of here; the kind Lowell and others have mused about eg "Here is the pair of Mountbatten Purdeys I bought on the weekend"...). The round "point" of the clip was not sharp, and stood wider than the barrel, though the surfaces did mate cleanly. I personally find the plain, flat, vertical breech face offers much cleaner, more elegant lines - especially with Woodward's arcaded fences! Less is more...
I can't see how they'd be a potential injury issue; if your finger or thumb are anywhere near there on closing (why? operator error) then it's going to be pinched against the standing breech anyway (trust me...!). There are myriad silly ways to injure yourself cycling any gun!
RG
