Is melee AA messed up?
Yes and no.
It's mechanically sound and works how it should.
However, it's strategically a terrible thing to rely on. A simple, weak-sauce slow can easily tank your DPS to 0 if your opponents have the presence of mind to not stand next to you.
Considering the amount of AoE slows out there, melee AA is also at a significant disadvantage from being bombarded by AoE team-fight chaos.
And of course being melee and sustained-damage based puts you in the front lines for a considerable amount of time, forcing you to spend ~6 seconds with a target to do 6 seconds worth of damage (where a burst champion only needs to get in range for ~2 seconds to front-load 6 seconds of damage).
As Tryndamere's melee AA's also push him towards being a glass-cannon, this is exceptionally bad - as he's the same type of high-priority target as a marksman, but he's significantly easier to focus and significantly harder to protect.
Melee AA's are nice in 1v1 situations where any fight is going to be somewhat drawn-out and you don't have 5 enemies dog-piling on a squishy though. When life steal comes into play in a 1v1, and opponent needs to 100%-->0% an opponent in one QWER, otherwise leaving them at 10% can easily allow them to keep stealing enough HP's to survive whatever additional burst you have access to when that comes off CD. The manaless factor of AA's also allows better kill-to-kill endurance than even re-seting burst kits.
If you can actually force 1v1 fights being restricted to melee AA's aren't to bad, which is where split-pushing generally comes in with Trynd. You split-push to force the enemy team to break up and generally avoid large-scale 5v5 fights from happening.
Anyways - 
is quite possibly the worst team-fighter in the game, but on the flip side he's quite possibly the best duelist in the game.
At least once you get ~3 major items on him.
The ~3 major items in paired with that basically means "not viable in competative play", at least with how the community uses the word viable.
If you know the strengths and weaknesses of Trynd you can force him to work though.
As long as you can get fury in lane, stay even in gold, and use his strengths while avoiding his weaknesses.
as a melee do i now have to get the hammer just to stick with someone that has over a 100 movement speed difference from me?
I'd just get Red Buff. Potentially the enemy team's via ward-scouting it and using 1v1 me brah tactics when the jungler tries to take it, at least once you're strong enough to try melee AA'ing things with Trynd (his early game is pretty weak).
Also - mostly champions are going to out-maneuver a Trynd if they have backup. The re-positioning tools and escapes available to most champions are usually a 1-time deal, where Trynd's joint dash and CC shout will usually allow him to catch up to anyone within a 1v1. Run with Exhaust and grab Kingblade and you're prey is screwed, especially if you crit them in the face while spinning in, giving you another spin. Which is more reliable if you approach things with max fury.
I've also found with using Fiora a lot in Dominion approaching targets in a way running up to them forces a flash/escape is something you always want to try doing.
You don't really want to use your jump to get on a target, as most champions will immediately cancel that with one of their skills - even non-mobile ones like Anivia and Morgana will just drop a wall or dark-biding you in the face.
Having your dash available to negate their escape rather than needing to burn it to reach them in the first place will let you hold onto more of your cards (and give you an extra bit of time to decide if going ham is rally a good idea at the time). Try approaching targets from their flank or sneak around behind them and you can really apply some serious pressure, forcing their escape/CC stuff out without even spending any of your cooldowns.
Dash at their face turn-based-combat style and you might get trollololol kited to death.
Using brush and fog of war really helps in flanking targets. Wards also really help so you can see them coming, being able to force a lot of advantageous fights with less power is more preferable than never being able to force an advantageous fight with slightly more power IMO.
TLDR: melee AA's suck in team-fights, so try avoiding team-fight situations.
