I wouldn't say I main Teemo, but I do play him an awful lot.
I agree with most of the things you said. Especially about his terrible auto-attack range. One thing to note is that while Sivir also has 500 range, she has a 1500 range skill shot that does great damage. While Teemo only has his blind which is very short range. Kog'maw and Twitch also have 500 range, but they both have an ability that increases their auto attack range.
I think Teemo's main problem is that MBR, one of his core items, is the weakest expensive items in the game and doesn't make him a threat.
You mention Teemo is not viable except for solotop, but I think he makes a good mid-lane player. Since most mids are AP, Teemo can easily counter build them early by grabbing a wit's end/mtreads. Teemo can also push the lane quickly without using mana, something that some AP mids are vulnerable too. Mushrooms give you a safety net against junglers, meaning the lane that is usually the most vulnerable to ganks is secure.
I know many players argue that mushrooms are annoying and that is what is keeping Teemo at UP status. Since, we have only to look to current Shaco to see the frustration caused by invisible traps. I'm honestly not attached to mushrooms that much where I couldn't play Teemo if riot reworked his ultimate into something else.
I will agree that Teemo is very outdated. I keep using him as an example to demonstrate champion powercreep. Since, every new champion gets 4 abilities that deal damage and they often have an escape that also deals damage, while a champion like Teemo has move quick which is vastly inferior.