Half-Life 2 in UE4? Sorta...

Honestly, I don’t think Valve would be too against a fan remake. I mean, they’ve completely supported Black Mesa thus far. I doubt a remake of HL2 in a newer engine would take sales away from the original.
It would just be a difficult matter finding enough skilled people to remake all that content from scratch, especially the voices.

Seeing those pictures made me wonder:

What would Black Mesa look like in UE4?

The way I see it, Black Mesa was okay because it was Valve’s IP in Valve’s game engine. The Unreal engine isn’t Valve’s, it’s Epic Games’, so they might have a problem with their material being turned into a game on another engine.

Then again, who knows?

Well EPIC want about 5% of the sales, so I doubt valve would allow that.
And Valve probably wants to sell their own engine aka source 2 instead of people porting their games to the unreal engine.

Assuming it would be sold. Originally Black Mesa was gonna be 100% free, until Steam Greenlight came around.

It wasn’t due to Greenlight. Paid mods have been on Steam way before it came around. Garry’s Mod is such an example.

Same with the free mods.

It basically all depends on how valve will react, but I doubt they’d oppose it.

I have desire to make Half-Life 2 Beta in Unreal Engine 4,but Unreal Engine 4.10 is too difficult to me including UDK.

Founded in 2004, Leakfree.org became one of the first online communities dedicated to Valve’s Source engine development. It is more famously known for the formation of Black Mesa: Source under the 'Leakfree Modification Team' handle in September 2004.