First you say that most FGs use the same kind of tech chase system like SG has.
		
		
	 
Read what I write and respond to what I write, not what you think I write. I said that in most 2D fighters you can block after tech rolling, which is similar to Skullgirls. Smash, 2D, and 3D are the major branches of fighting games and all have different implementations of tech rolling, all of which inspiration can be taken from.
There are more aspects to tech roll game and okizeme than "tech roll, not tech roll, can block or not"", and there are lots of ways Skullgirls' tech chase game could be altered. I'll list a few games that do tech chase game differently. Also, I will consider air tech as okizeme/tech chase game since it is effectively another method of setting the same kind of situation up.
Guilty Gear: Every knockdown is a hard knockdown, air tech chase exists. This makes oki strong and air resets not as reliable strong but still possible. In Skullgirls, it is the opposite - no air tech chase exists allowing for guaranteed setups, but hard knockdowns are rare. Clearly a decision has been made to prioritise one over the other in both games, and I personally like the air resets in Skullgirls.
They are both fun and unique. The problem is that they make tech chase redundant as a mixup option, but tech chase is there if you want a large chunk of damage to result in a knockdown+lower your opponents undizzy if they tech+get a mixup of some sort after, but risking the fact they could escape your mixup.
Third Strike: No air tech, you just get air reset with no air actions and being parry and get hit. Ground tech = stay on the ground or tech backwards. Mostly affects meaty timings and sometimes cross-through setups. I am unaware of any other properties stay down/quick getup have. Someone please educate me if I am missing something.
King of Fighters: Air resets cause you to not get hit on the way down and lose throw invulnerability when you land(as far as I know). Knockdowns can either be hard or soft. Soft knockdowns let you tech roll backwards, but tech rolling backwards has you give up your throw invulnerability on wakeup. This interacts with the game's throw invulnerability after wakeup or leaving blockstun mechanic by giving you a choice in what you want to deal with.
Skullgirls is unlikely to gain any sort of throw invulnerability mechanic because throws already start up slower than jabs. The common thing between 3S and KoF is that you can only tech backwards, which in SG would basically make tech rolling meaningless since it would just corner you and no-one wants that shit.
Virtua Fighter: Depending on the kind of knockdown you are put into, either a knockdown from an attack or being put into a grounded state through a throw, you have different options. Knockdown = Press 3 buttons as you land to instantly tech into foreground or background. You can choose to not tech to be put into grounded state. Get put into grounded state, you can choose to neutral getup, back, foreground, background get up roll. You can do an invincible on startup getup kick after every single grounded state tech option that isn't neutral get up, which can get beat out by moves that do more damage that trade with it (universal game rule).
Virtua Fighter's method has extra dimensions due to the 3D nature of the game but it's a bit of a red herring. The important part is that you have multiple states you can tech from which give multiple options (Tech as you hit the ground from a move that doesn't put you directly into grounded state, or wait until you are in grounded state) from multiple states, as well as a character-specific invulnerable getup move that is able to trade and therefore can be beaten by higher-damage trade setups. In older Virtua Fighter games, this invul getup attack was punishable on block but in FS it just puts you into a 50/50 situation. Only one other 2D fighter I know of has invulnerable get-up attacks for characters, and that was Waku Waku 7.
Invincible getup attacks might be something to consider, but is unlikely due to the fact that characters already have invulnerable moves that work like getup attacks and also tend to be heavily punishable on block without meter expenditure.
Being put into a grounded state for longer before you can tech roll might be something Skullgirls could implement, since you can tech on both blue bounces of a blue knockdown. You could make it so that if you tech on the first bounce, you get an instant left-right tech. But if you wit for the second bounce, you can't instantly tech from that. Instead, you are in invulnerable knockdown and have ~15 frames within that knockdown state to chose neutral, forward, or back roll. This would be an interesting experiment to do, actually.
TL;DR
My actual VF-inspired hypothetical suggestion for altered SG knockdown is:
For the second knockdown in blue bounces, make it so that you have to wait 10 frames or so in an invul knockdown state before choosing to neutral, forward, or back tech. This would make knockdown/tech chase game stronger for more characters while retaining the victim's ability to quickly gtfo on the first bounce.
Edit: Also more moves could put you directly into the second blue groundbounce state to facilitate that kind of tech chase, like sweeps.