I agree that the gameplay in such scenarios isn’t much enjoyable.
Anyway, it’s usually the same for the opponents. There was one match some time ago where I literally spent 4 seconds in lane, Back, run, one ability, Back, I literally didn’t have done anything. But, it made the difference for my hero takedowners 
and we got an advantage and won.
Unless the match is lopsided, in which case lay back and let it end and blame it on the design.
All those heroes you mentioned are useful in QM.
That’s what I was thinking too - Azmodan, Hammer.
Instead he goes on to list some of the more mobile bruisers around. Honestly, it’s a L2Play issue, especially in Dehaka’s case, as you go into the fight with 3 HP bars post-10. Mobility? 40% speed for 5 seconds whenever you are near a bush is faster then even regular mounts. Dark Swarm prevents you from being body-blocked. Drag prevents them from running away.
So, some Dehaka tips.
Tip 1 - Unless you picked CDR on Drag at 7, which gives you an effective 5 second CD on Drag, save Drag to secure kills. Do NOT use it on full-health targets - You’ll get them down to 70% health, and then since you completely lack follow-up CC, they just waltz away. Instead, you use Dark Swarm, AA, and stutterstepping in order to avoid ability damage, and Adaptation+Trait to soften up targets. When they start running, THEN you use Drag. So many Dehaka’s just try to Drag the first target available, miss, and then can’t do anything.
Also, you need to practice Drag (And all skillshots, really) to the point that you only miss it if the opponent uses one of their own abilities to get out - Either movement ability, or cleanse. If you get juked, you just got outskilled.
Of the heroes you mentioned…
Nova, Jaina, and Kael’Thas has 0 mobility. None.
Dehaka is Abathur’s bane - Against even a somewhat good and aware Dehaka, Abathur can’t even leave the town hall.
Genji is all about knowing his abilities - E up? Trait up? Go to the nearest bush then 40% speed to get him to GTFO. Once both E and Trait CD is up, Genji is ded.
Li-Ming only has her teleport - Dodge the incredibly telegraphed and easy-to-dodge Ws (The only time that I get hit by W is when an idiot teammate bodyblocks me, and Dehaka doesn’t have to worry about that), and go to a bush to speed over to her and kill her.
Really, the only 2 actual threats to Dehaka, rather then just free kills, are Tracer and Orphea. You honestly can’t do anything about Tracer tbh - She’s basically the bane of all melee who don’t have point-n-click CC (But at the same time, she’s countered by every range AA hero around).
Orphea is a complete measure of the skill of the player behind her - If she misses even 1 Q, she dies. But if she lands all her Qs, you die. Hint - E makes her miss a Q.
Lol you typed this massive long essay and from your post I already know you’re playing against really bad opponents.
You’re hitting drag against the heroes I listed? Tracer, Li-ming, Nova, Jaina, Kael’thas.
The only way that’s possible is:
It’s number 2 unfortunately
Against Nova, Jaina, and Kael’thas, who have NO mobility at all, and are completely reliant on CCing you, you should be able to hit them with drag if you are in melee range.
Against Li-Ming, you get into melee range, she teleports, and you just chase. Because you get 40% movement speed for 5 seconds.
And I did state that there isn’t much of anything you can do against Tracer, who is THE counter against any and all melee without point-n-click abilities.
The way it sounds, you are the one currently playing and stuck in wood league. Get up to at least plat before you talk big.
As a QM enthusiast, what ever pain you’re facing the enemy team is typically facing the same problems.
You can’t live long so your engages have to be even more precise. Dehaka is a luxury, times are tough when the team is relying on you to engage as ragnaros or thrall.
Or a malthael lol that’s even worse
It’s an easy fix, delete QM and make unranked the new “qm”. Just rename unranked to QM.
Just make picking heroes shorter and disable bans and disable wanted roles.
Sadly, i trust QMs ability to make a team over the brain power of some players.
Well, the QM MM rules main priority is a tank and a healer in a match,. Other 3 are wildcards. If no tank and or healer is found, then it’s all wild cards.
Rather have stupid players than a very stupid MM system
Unranked draft is the least played mode and has the longest queue times in many regions… If you look closer you see there is another draft mode called Stromleague (basically the only real draft mode).
Don’t be afraid to play Stormleague, i know it says ranked but you should know that it’s just a ladder and everyone will have a place on it.