A Blade is deadly wherever you are. Period. I would say though, the only reason I would say going to the ground is worse on the scale of deadly, is because I have eliminated the option to run. IF you fight a person who knows what they are doing with a knife, and you have no weapon, you are up shit creek. If you know you are doing and they do not, and they are committed in attack, you are still likely to bleed, alot. The only upside is it is not a gun, and a person does make more power with it, stopping power (liver, kidney, heart, etc) thrusts are easier to get with full leverage (meaning standing), So you will get cut up grappling a person with a knife....but guess what, if they have a knife and you do not, you are likley to get cut up anyway. So I agree regarding train the best you can, and most of the time I spend grappling more these days has more to do with impact being harder on the joints than what I feel if most practical for a street scenario. Because the true reality is, the "street scenario" is extremely, extremely rare in a first world nation unless you just want to fight in bars, or you go to too many "peaceful protests".
Grappling certainly has it's place no doubt about it. But tactically its the worst place to go unless you've no other option or get dragged down.
There's lots of things to consider:
Dangerous uneven surface.
The concrete is effing hard, and if you go down badly you could be looking at an injury. No light canvas to break your fall.
Detritus - Broken bottles, syringes, etc.
Also, if there are two assailants. His mate could stab you or kick you to death while you're engaged - that actually happened some years back to UFC guy (got stabbed by the opponent's mate from behind).
You're critical focus will be compromised and focused on one opponent (tunnel vision, adrenaline, etc).
Compromises one's ability to escape.
Like I said, you train for it but you don't aim for it.
Re. Knives, a person who 'really knows' what they are doing with a knife - Then you can pretty much kiss your ass goodbye. AKA - a two handed knife fighter. Someone who uses their 'off hand' in order to use their main hand to stab. Mind you, even a drooling drunk lunatic with absolutely no training whatsoever is still very deadly. Especially if they panic. They will go sewing machine on your ass (especially if you try and hold them).
In all honesty, to this date, I've never seen ANY system that can deal with a knife 100%. Yeah, you might very well get cut - It's about mitigating the damage by attempting to cover your vital areas. Easier said then done of course. However, there are some principals that are light years ahead of that Kratty Fu shit where they just simply pluck the knife out of the air. LOL. I'd love to see someone try that outside the Dojo against a committed knife wielder with real intent.
Running is always the best option... As I said before. Fighting is a mugs game, best reserved for the school yard and scum bags. Unfortunately, even in a 1st world country there are still plenty of violent scum who venture into nice places. I know many people who've been violent attacked in Dublin city for doing nothing more than minding their own business (some even in broad daylight with lots of folks about). And it's only going to get worse as the economy takes another nosedive with this whole pandemic thing. Shite bags have got to have their drug money.
Also, if it's part of your occupation you don't always have the option of running or walking away. For example I worked as a bouncer for three years in the UK to put myself through art college (in my twenties). I never had the option of just walking away unfortunately. Luckily we had a good team of guys.