All of these points sound great to me.

PLEASE bring back Lara’s home

I want to go back to explore the cliffs of Bolivia, the tombs in Egypt, the jungles of India, ruins in Nepal, and temples in Ghana and Thailand. I want that Indiana Jones sort of adventure where you have to get through booby-traps and the wild wilderness in order to find all sorts of hidden keys and maps that lead to amazing treasures. And I want to go back to Lara’s mansion. That definitely needs to be brought back in the next installment!

I agree with Chamberlain. Any time someone says “if you don’t like it don’t play it” I direct them to games like Spec Ops: The Line. That game is criminally underrated and received lower reviews than it deserved because the multiplayer took away from the overall package. In fact, it infected the development studio itself. They had an interview with Polygon posted on VG 24/7 that makes for a very good read about the whole process and how it can ruin games –
http://www.vg247.com/2012/08/29/spec-ops-the-lines-multiplayer-is-a-cancerous-growth-says-yager-staffer/

Especially in regards to Tomb Raider – it was supposed to be a game about a girl overcoming her weaknesses and finding a way to survive, against all odds. The multiplayer was just a band of random people shooting at each other for sport with shallow game modes and weak mechanics. To me, it hurt the overall package.

Sometimes including multiplayer can take away from the main game, who knows how many people and how long it took for them to make that multiplayer part. All that time and effort could have been made improving the singleplayer aspect of the game.

playing the multiplayer mode, it gave me something to do during
the post-game (another point I probably would have mentioned – the lack of
postgame definitely disappointed me). Granted, when I bought the game, it was
solely for the single player experience and having the multiplayer included in
the game never once took that away from me. The single player was fantastic and
I enjoyed every second of it. The fact that the MP is included in the game
isn’t a bad thing, especially considering it’s quite a decent online
experience, but the fact does remain, if you bought Tomb Raider, you bought it
for the single player, not the MP.

If you didn’t want to play the MP, you don’t
have to; the core of the game is still there and to me, the MP is merely
additional content to keep the interest around. In fact, I commend Square Enix
and Crystal Dynamics for introducing this. I’m not a huge fan of trading in my
games, I like to keep them, more for nostalgic purposes, but I really don’t
like having games that can sit on my shelf collecting dust, knowing that
there’s no replayability unless I go through the campaign again.

Everything else you
said, I agree with 100%, but the multiplayer in Tomb Raider has never once
taken away from the single player experience, and for that, I don’t think
removing this from the next instalment will be of any benefit.