That being said, after some research into the proposed solution of the Bitcoin core team,
The lightning network is not something that was proposed by or being worked on by Bitcoin Core developers.
For example, even though in the whitepaper for Lightning Networks (LNs) the development team specified that a blocksize increase is still needed, why is there so much resistance to using it now to mitigate full blocks?
Because we don't know how Segwit and the deployment of LN is going to effect the economy and the transactional capacity. There are consequences to increasing the block size (and there are positives to having full blocks and a mempool that is not emptied on every block) which we do not think are worth having for a larger block size limit. The lightning network is not yet deployed and increasing the block size limit further may be more harmful than not.
This creates a new and powerfull actor in the Bitcoin economy: these liquidity hubs. They can broadcast, or not broadcast when they want to the main chain.
Not really. The people who are connected to those hubs can close channels any time that they want. So if a hub is being a dick and refusing to close a channel, then you can close it yourself, albeit you will need to wait a little bit before you can access your coins. Likewise you can do the same the the hub. Furthermore, if a hub were to be engaging in that behavior, many people would likely just stop using them. They would close their channels with that hub and route payments through someone else. Anyone can be a hub, so there likely won't be a shortage of alternative hubs to use and that people are simultaneously connected to.
Furthermore, the most experienced and trusted source of LNs will become Blockstream who can therefore probably build the best LN.
What makes you think that? There are at least 2 other organizations besides Blockstream who are building software for LN. They employ more people than Blockstream does and all of them are collaborating on making their software compatible via the Lightning RFC spec.
In the best case scenario there will be a handfull of these LN providers, is this desirable? Blockstream would be behind core, the main LN and could have influence over miners through non-broadcasting, is this desirable?
You overestimate the manpower and influence of Blockstream.
First of all, as I said earlier, anyone can be a LN hub. You don't and shouldn't be connected to only one hub. There will certainly be other hubs set up by the other LN developers for people to use.
Secondly, Blockstream is not behind Bitcoin Core nor do they control Bitcoin Core in any way, shape, or form.