No you do not have to pay to do a key but it will take patience to apply.
I see most of the obvious things have been pointed out like dps are the most plentiful role, so the most competitive when vying for a spot in a key.
Leaders will look at is your score, your ilvl, general experience, your main’s score (if relevant) etc. Anyone can build up score. If you are really struggling to get into other people’s keys it may be worth just pushing your own key instead or joining a key community.
I don’t want him there if he’s one of those who always complain every single pull 
People care juat about rio and ilvl. Better rio and ilvl = better chance for invite.
This season is fairly easy to get +20 in.
Implement matchmaking and queuing, like all other games have. Not slap the queue on existing M+ system, of course it won’t work. It needs full revamp of key concept, scoring, mechanics, difficulty scaling, composition matchmaker and so on to make it queueable.
There’s nothing wrong with the group system as far as I can see it gives me a list of applicants and I pick the ones that I feel would be best suited, and they get invited, working as intended.
The simple truth is it’s a numbers game, if I am hosting a key (which by the way is how I don’t wait for hours, if I’m not running with my guild, I host my own key so I always get a spot) I will choose the players from the literal 100s that apply, that I feel will give me my best chance at success.
If you are struggling for hours to get into a key, (I’m on a big server and I’ve never waited hours, maybe 20 minutes before someone invites me), run your own keys to raise your score and appear as a better proposition to group leaders in order to get picked more.
make ur own key
Like 10000 other players. What makes you special? 
Perfect karma for all the times you’ve trolled threads with “just pay for it”
Yea, if you lack skills to get into a group pay for it by all means. It’s a you problem, other people seem to manage.
I notice you say you have 480 but make no mention of class, spec or role as potential contributors. Yet me with a 473 dps alt got into a key np’s yesterday without paying.
You can avoid paying 140k by waiting and seeing if the price comes down. I’m doing that with Curve. The main trade spammer on my server has lowered their price as the season has gone on.
But imo you’re missing one essential thing here… WoW is not “like all other games”, WoW is an MMORPG… Treading it like LOL or CS:GO, would just be taking the genre and slapping it up…
I would rather argue, that people should get back to socializing, building communities, guilds instead of this “I want to log on and have insta ques alone!!” mentality…
Correct me if I’m wrong, but there is no similar gamemode to M+ in another game, that allows you to just que up with a matchmaking system is there?
So while I do see your point, I fear that the implementation of such thing, would have the same effect as in Solo Shuffle… It becomes an even more “solo” game, and it just deters people away from wanting to play the game mode…
Aren’t you missing a third option?
I honestly wanna know the OP’s solution for this. Like really.
You’re just complaining cuz you didn’t get invited into group. I could cry a river if I would start about how many times I didn’t get invited as a dps.
There is sometimes over 50 dmg dealers applying for one keystone. It’s not a bad system, it’s just the system. If you wanna make sure you’ll have run after one another, just make your own group, invite the people you consider relevant for your keystone.
Join the guild, do the guild runs. There are other options to get into m+ or raid run.
Crying on the forum will not solve your problem. Cuz for me it seems you are just waiting for insta invite.
You can have 3k+ score and you’ll be still competing with bunch of other players in High Keys.
Having high score doesn’t automatically mean you’ll be invited. It’s just higher chance but not 100%.
If I’m forming a group where I need dispell, or special ability to deal with affix or Lust/TW I’ll gladly consider taking someone who has lower score or ilvl over someone who has legendary and 3k+ rio … easy as that.
You have at least 6 options.
Join a guild that meets your m+ needs, plenty of m+ guilds exist (this might be server dependant at least until x-realm guilds come in)
Create a guild that meets your m+ needs (this is more long term, but is a solution)
Join a community that meets your m+ needs
Make a community that meets your m+ needs
Run keys with your battlenet friends
Run your own key
None of which involve waiting or buying a boost, all of which will have some degree of success, and as you complete more keys, you’ll also get more invites.
reroll to tank and get instant invites 
It is approaching 100% after applying to 50 groups though, as the OP claims he had to do. :'D
But yes - of course humans are not inherently predictable. I cannot guarantee a 100% for certain invite. No one can.
Just running your own key seems the best yield for the lowest effort. You’ll notice you can cherry pick the best yourself, and understand a bit more why dps is a hard role in that regard. Just throw the lead on the tank once the key starts if you don’t feel comfortable in the role.
I’m gearing a hunter atm and once I get to 460ish I plan to do this for keys 15-20. Nobody cares below 20 this late in the season.
Score, ilvl or parsing is not the issue.
My Lock is sitting at 28xx score with 485 ilvl and my DPS is not bad either, yet, it takes me around 30 minutes to 45 minutes find a spot in a +20 key.
For better or worse, to find a spot quickly, you need to:
IMO this is a community issue. As someone that played Guild Wars 2, even high level fractals (its like the M+ of GW2) were very easy to get in. Only VERY EXTREME HIGH END people would cherry pick the “meta” specs.
I agree with people saying that the 3 bullet points I’ve counted are not ideal and indeed they are not, thats simply how it is. WoW has a small but loud minority that defend its negative sides brutally, with usually condecending attitude, so everytime a subject like this comes up, expect a lot of “banter”.
It is not a community issue. Especially not for +20’s. I do not see people asking for meta at all on those keylevels. It is a matter of having instantly 50 dps singing up when i post my key. It is an issue people create topics here demanding instant invites. They do not understand when i invite them i have to disappoint someone else over them. And from those 50 applications i have to disappoint 47 anyway. There is no spot. That is the reality. I would like to hear a solution so i do not have to disappoint 47 dps.