Long slow distance work doesn't have to be running.
Just saying.
The idea of steady state cardio as merely a base for high intensity is inaccurate. I went through a phase where I only did high intensity hill sprint intervals for conditioning, when I added steady state cardio back in once/twice a week I saw an almost immediate improvement in terms of quicker HR recovery between intervals, the ability to do more intervals in each session and the potential effort to reach max HR.
They're complimentary and necessary. If you're only doing one you're missing out, but I would definitely not do them both in the same training session.
Forgive the oversimplification but intervals mimic the cycle of max effort-> recovery->max effort. Steady state cardio is what allows you to keep repeating the cycle for longer periods of time.
Grappling is dependent on raw strength and boxing is more dependent on conditioning; power in boxing is more about technique than raw strength, conversely you won't get anywhere in grappling without raw strength that's why it's a different kind of "gassed".