There used to be some room for high priorities transactions, which even don't pay fees and will be confimed in the blocks with other paying transactions. In the mean time miners seems to only include the higher fee one in the blocks and ingore the high priority ones. What do you think about it? After the block is increased, will this function be activated again?

As to me, just setting higher priority makes no particular sense

Besides, as far as I know, priority depends on how long a transaction hasn't been confirmed, and that might make some sense after all. Other than that, the only genuine measure that could objectively set the initial priority is the size of the fee itself. Really, if you want to prioritize your transaction and make miners actually pay attention to your needs, you prioritize it by making it more valuable for them to include it faster in the next block. In other words, you should put your money where your mouth is

This function is still active! But why would a miner pick someone who's sending a million dollars without a fee, if he can pick someone who's sending 5 bucks with 1 dollar fee? Of course the miner picks the transaction that earns him a dollar over the one that earns him nothing.
For the future when blocks might get bigger: Bitcoin Core 0.14 will deactivate this priority mechanism. (I only read this recently, I can't find back the source, so don't hang me on it)

Priority for sender and receiver but not for miners, only priority for miners is a transaction with the highest fee, time where miners gasped for some txs to include and those faucet big transactions were considered a fat bonus has past and are now a history.

Touché!

That's the "whatever metric they want" which seemingly isn't located inside the sphere of "public interest" which includes everyone of us.

It is the same in any field of human activity

People are doing something (or just anything) not because of some obscure "public interest" but rather out of their own private interests (thiugh that's normal). And miners are not an exception to this rule anyway (but this alone doesn't make them less evil, of course). Mining starts to serve public interests when competition kicks in so that miners can't raise their fees infinitely. But since competition in this field is close to being extinguished, we see all the ugly effects of a market which has been heavily monopolized

Higher priority transactions are now useless and there is no room for that anymore. The ony thing that matters now are the higher fees that you set on your transaction so you can have a fast confirmation. Without a higher fee that is set  your transaction will not be prioritized. The only VIP in the network are those who have the capacity to pay a higher miner fee.

Interesting do you have know where to find the update log for that the last I recall it was coinage that determined the priority of lower fee transactions.
Simply put older it was the less the txt
https://en.bitcoin.it/wiki/Transaction_fees#Historic_rules_for_free_transactions

(Edit in:) Looked at the 0.1.2 log see where this was introduced

Bitcoin Core has a heuristic 'priority' based on coin value and age. This calculation is used for relaying of transactions which do not pay the minimum relay fee, and can be used as an alternative way of sorting transactions for mined blocks. Bitcoin Core will relay transactions with insufficient fees depending on the setting of -limitfreerelay=<r> (default: r=15 kB per minute) and -blockprioritysize=<s>.

 In Bitcoin Core 0.12, when mempool limit has been reached a higher minimum relay fee takes effect to limit memory usage. Transactions which do not meet this higher effective minimum relay fee will not be relayed or mined even if they rank highly according to the priority heuristic.

Seems like a bad adjustment in my opinion as it favors miners and fee gathering but does not account for people who rarely use the network to send and are not a big part of the bloat issue.

Correct. Whoever assumes that all miners are genuine or working towards the common good is confusing Bitcoin with socialism.

They lose out additional money, i.e. fees per  block. There are heavy debates on how much extra propagation time and risk adding TXs to a block includes than just mining an empty one. With empty blocks it is less likely that you're going to lose the 'race' to someone else.

That is it: You can't. The miners can't be forced by others to do what they like.

There is a limit to all of this. They can only prioritize so much. I'm assuming that some miners already have *private* offerings for "premium seats" in their blocks.

And this requires a fork, which needs support from miners, ergo you can't force them to do anything.