When I see Kickboxing I assume Muay Thai or Dutch/Japanese (K1).
You learn knee and elbow strikes and clinch (neck wrestling) you won't believe how much quick damage they can do especially from those who have trained properly under a good coach even for a short period, You land either one of those on someone which is a lot easier than you think when you're in each other's faces and your would be attackers are untrained, People are going
quickly or they're getting extremely bad cuts, Out on their feet and broken noses, orbitals and jaws.
Let's not forget trips and sweeps that are learned, they fucking hurt on concrete.
Why not learn both and be competent at boxing elbow knees kicks, If you break your hand which is quite easy in a street fight people's skulls and faces are harder than you think, What you gonna do???
Also if you're in a good Kickboxing gym your boxing skills should be very good anyway, Since when did Kickboxing become Kicking only? Elbows and Knees are disgusting and put people out quick.
You want to be well trained in forms of fighting/self defense that's quick powerful and explosive as the longer shit drags on the more likely you're gonna get overwhelmed and then fucked up, especially on solid ground good luck doing your BJJ or Wrestling on the car park when 3 guys are throwing hail Mary's at you and want to kick your skull in.
Boxing for sure is very very important but you also need your close range weapons and that's why Muay Thai and K1 is gold standard.
I'd still learn to wrestle and grapple though because in a 1 on 1 good luck against a grappler who can strike, plus it improves your balance and posture strength beyond words