Lumbermills make almost no sense. Why would you wait 3/4 of the game to finally get some decent production of of a tile? By chopping them you can rush early buildings, and by mining over them you can have 300+ turns of good hammer production, over the course of the game thats a ton of hammers more than just leaving a forest. By the time lumbermills come along I already pretty much know if Im going to win or lose, Ive never had a game where I was like 'wow lumbermills, finally i can go on to win this game!'. Plus the health loss can easily be rectified. Basically they have no redeeming aspects at all for me.
With StateProperty pretty much dominating the scene, theres even less reason to keep them around.
Well, in BtS, State Property is going to be a lot less attractive. No corporations means that you're going to have a potential handicap. Also, There's a lot to be said for Free Enterprise if you have a good economy and there are a few AI civs that also have good economies for you to trade with.
If you don't like Lumber Mills, that's fine. Personally, I find that I am not going to use all of my tiles even in my capital, so leaving a few forests behind is just fine with me. I'll be working those grassland Towns, Farms and a few Mines before Replaceable Parts. Once Replaceable Parts kicks in, I'll very much enjoy being able to kick in some extra production and I especially like having a massive production city in the middle of a vast flat land just because I remembered to leave behind a few trees.
It's also entirely possible to end up with Replaceable Parts before Chemistry. If you know that an opponent is going for Military Tradition, then you might want to make a run for Rifles as a counter and wait a bit for Chemistry. That means 2F, 2H for a Grassland Forest vs. 1F 1H for a Workshop. Even after Chemistry, it's 2F, 2H for Lumbermills on a Grassland Forest vs. 1F 2H for the Workshop. It's even worse for Plains.
Lumber Mills are certainly not the most exciting thing that you could possibly have in a city. It think that honor goes to properly teched out Watermills or fully developed (and appropriately civic'd) Towns. Lumber Mills aren't such a bad thing to have around, though.
Remember, you're probably going to have Replaceable Parts long before you get to read any of Chairman Mao's little red book.