The left (both modern and not) is much less self-defense averse than you think. There's plenty of leftist gun clubs; the Socialist Rifle Association and Redneck Revolt, formerly John Brown Gun Club, come to mind immediately.
There's also the long history of unions literally going to war against capitalists, like in the Battle of Matewan.
Also worth remembering that leftist groups like the BPP encouraging its members to legally own firearms led to significant gun control expansion in California.
Depends on your definitions, right? What you describe sounds an awful lot like the Democratic party, but they're liberals, not leftists. I'd argue they're center-right.
From what I've seen at least, when more leftist parties like Green, DSA, the various communist parties, etc, talk about reducing gun violence it's in the context of eliminating poverty and other environmental contributors to the problem.
There's also the long history of unions literally going to war against capitalists, like in the Battle of Matewan.
Also worth remembering that leftist groups like the BPP encouraging its members to legally own firearms led to significant gun control expansion in California.