And not forgetting Dragon Age 2. Would love to see the complete DA collection here.

Yes, publishers are begging GOG to let them release their not so new AAA games here, but GOG stubbornly refuses their pleas.

/s, just in case

I would guess that of course GOG does what it can so that more games (AAA or not) find their way into here. What store (digital or not, gaming or not) wouldn't want to sell more things?
But those games' companies (publishers and/or developers) don't always want their games sold here. They obviously prefer DRM (rental) platforms, than "you download it and you keep it forever".

But GOG's methods for acquiring top tier premium games clearly are not working the vast majority of the time.

Therefore, their methods need to improve in order that they might finally become effective and therefore fix GOG's #1 problem, which is the scarcity of high quality games on offer.

The best way for that to happen would be for GOG to disclose all of their methods here on this forum as to how they approach publishers/devs, and what exactly they say to them, and what kinds of statements they receive in response, and then let the community give them feedback as to what they are doing right and wrong and what they could be doing better.

Kudos to you for knowing Takeover, game flew under the radar even for many arcade/beatemup fans. Sky force might be a mobile shmups a bit on the casual side, but it's pretty legit too.

I don't think that everything can be said, some (most) things may have to stay confidential between the negotiation parties. It's like football transfers, for example! We don't always know why a player agreed, or not, to come to our favorite team!

In publishers/developers/other right-holders' oblivion. They definitely don't want to waste their efforts for bringing the games to GOG-acceptable state: cutting all online features (account binding etc.) and re-licensing all third-party components (cars, music, brands etc.).
First case is illustrative for Battlefield: Bad Company 2 that'll soon be removed from other stores cause of expired multiplayer support (even single-player campaign), second - for Need for Speed mentioned by you.

we are talking here about older games that no longer have an online mode or players looking for someone online

Electronic Arts and Ubisoft have basically stopped releasing their "newer" games on GOG since they took up their respective launcher shenannigans. That's 2011 as a hard break for EA, and a rather softer one for Ubisoft since 2009 (Rayman Origins released here, and it's a 2011 game). It's not just the AAA stuff, mind you. I'd give two toes for a Child of Light release on GOG.

That covers most of the games you mention.

The problem is not GOG's, definitely not. All they can do is keep asking, and I would presume that the "advice" they'd be getting from GOG's fans would be to be more aggressive and to put more pressure on these publishers, which is a surefire way to kill off any chance that these games finally release here.

The only advice I could give would be to not belabor the point that EA or Ubisoft would make a lot of money by selling 10+ year old games on GOG. They clearly would not, and they have those statistics from working with GOG this last decade. But it would be an act of preservation of these games, and an act of cultural reintroduction. The reward would be the legacy of those games and the company.

I haven't been able to play my disc version of Mass Effect 1 and 2 since switching to Windows 10. ME2 was one of my favorite games and I probably completed it half a dozen times. Damn, I'd be over the moon if EA decided to turn the ship around and release the updated version here.

A variety of factors, but it all comes down to priority. GOG, having nothing substantial to offer to the big companies, will naturally get the short end of the stick and maybe receive a few big games per year.

They don't have the rights. There are confidentiality rules between commercial exchanges with companies. Signed between companies but also at the level of law in general.

They can still get around that by speaking in general terms, without naming names as to which company said what exactly.

Like instead of GOG saying "Ubisoft said this," they could say, "one publisher said this," or something to that effect.

But there are many variations as to how, exactly, an "ask" might be performed. GOG could certainly change the how of how they ask.

And how could GOG force the publishers to release them here?

If they don't release on their own platforms, they usually only have $₮€₳₥ in mind.

It's most likely that EA and Ubisoft simply do not want these games to be (re-)released DRM-free on GoG.
GoG would absolutely jump at the opportunity to (re-)release them but if that opportunity never materialises with EA/Ubisoft agreeing to these games being sold here then there's nothing GoG can do about it, other than reaching out to EA/Ubisoft again and again.