What is Teemo's identity? Why is his Ultimate so weak?

Before we dive into the discussion about Teemo, here's a quick summary about who I am and why I may be a decent source of info about the subject:

• I have played Teemo in every role imaginable with much success in both Top & Jungle.
• I have been maining Teemo since 2011 - I've played thousands of games with Teemo only.
• I currently have over 1 million mastery points combined on Teemo when I add all of my accounts.
• This season, in terms of Rank, Hikashikun and HLkashLkun are both Masters whereas HikashLkun is currently D2.

Anyways, this season has really gotten me confused about Teemo's identity. Like, is he a Marksman? A Mage? A Tank? A Split Pusher? A Rock? He's too weak to build solely AP as any other regular mage would thanks to the nerfs on his ultimate making it extremely risky rather than rewarding because for one, his ultimate can be easily disabled and destroyed by red trinkets (why can't this function work for disabling Caitlyn's traps?) and pink wards. Secondly, they don't nearly last as long to be useful in terms of effectiveness and impact. However, because Teemo's damaging abilities scale with AP, we're forced to build AP and even CDR to try and maximize his damage potential but we're still left with too much risk and very little reward therefore, we're being punished or put at a disadvantage to build accordingly. This has caused many other Teemo mains to build other items to remain remotely relevant such as Frozen Mallet, Runaan's Hurricane, etc., items that don't even add any value to any of his abilities; they're just there to add other utility such as wave clear or tankiness to his otherwise poor set of skills and stats.

Anyways, my suggestion to Riot is to either change Teemo's (R) Noxious Trap to last longer, cost less mana, and arm themselves faster or make his (Q) Blinding Dart scale with both AP and AD, similar to Jax's (Q) Leap Strike.

Also, I know that on PBE they are buffing Teemo's ultimate but they still don't address the other half of the issue, that being the mushrooms taking too long to arm themselves.

So many times have I tossed a mushroom on a jungle camp and as soon as I auto the creeps, they pass right through the mushroom without even activating it. Also, the bouncing mushroom thing is still so damn useless, I rarely use that mechanic at all. Like, what is the point of the bouncing mushrooms again? I can bounce mushrooms into the enemy? But don't they like take forever to even go invisible and arm themselves, allowing the enemy plenty of time to take them out? I love tossing the mushroom part but loathe the bouncing.