No need for the burger analogy, because I'm similar to you. I grew up playing Afterburner with my dad in the arcade, staying up late on weekends to try and finish Sonic the Hedgehog with my dad, playing Virtua Fighter 2 until it came out of my ears, ringing the shop every week to ask "is Shenmue out on Dreamcast yet?"... Even a few years ago I purchased all three Shining Force games in Japanese and then installed Saturn emulators on my PC and plugged in a SF4 pad so I could finally play the trilogy in english! I think it's fair to say that Sega has played a big part in me getting into gaming and enjoying the medium and yet, if they were to exit the market I would happily continue playing. Gaming is, and always has been bigger than just Sega.
For all the negative things I say about Sega, and how I get disheartened with their decisions, Yakuza, Bayonetta and VF5:FS are some of, if not my favourite games this gen. Even so, The Witcher 1 and 2, King of Fighters XIII, Mafia 2, Max Payne 3 and more were also games that I absolutely adored. I guess I just can't understand it from my perspective, because why would I refuse to play The Witcher 3 just because Sega isn't making Yakuza 6? I wouldn't turn down King of Fighters XIV just because I can't play Virtua Fighter 6.
Not to mention, Sega's best titles and developers would likely be picked up by another Publisher anyway.
The fact is, your hamburger analogy is flawed. You aren't not eating at a certain restaurant because they don't make the burgers anymore, the equivalent would be saying that because they don't make a certain burger anymore, you will never eat any food ever again.