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The best heavy armour can be better than the best light or medium, but the issues are how rare and hard to obtain they are, their weight, and needing to skill link on most characters. Each of the best heavy slotted armour pieces is only dropped by like 1-2 enemies each, at low odds, while plenty of enemies drop some of the best medium and light armour. And since having the best armour makes relatively little difference most people don't both.
Shulk could be best with Heavy for instance if not for the fact it costs him 15 coins to link, and also increases his weight a bit. The extra weight isn't a big deal postgame (4 weight = 1% less hit rate, and Shulk can get 100% or near 100% hit rates with a little investment)
Reyn can go Lancelot or heavy stuff lategame, he might want to link weight reducing skills though to help a bit with his hit rate against postgame stuff.
Sharla has middleweight expert which generally makes Lancelot best, but some heavy stuff is still superior.
Dunban has 15 weight reduction, so he actually does well with heavy gear. He has lightweight expert but the lategame light armour is pretty bad.
Riki probably is best with heavy gear. Not much need for low weight and he can equip it easily.
Melia needs to link the equipping skill but does have Heavyweight expert. If you need her to have more survivability, heavy gear is decent on her, but personally I tend to use the coins for other things.
To give an idea of where the best heavy gear is found, just take a look at the drop lists on the wiki (note the Wiki's drop rates are wrong, though they tend to be at least around the values listed): https://xenoblade.fandom.com/wiki/Rex_Helm https://xenoblade.fandom.com/wiki/Rex_Chest https://xenoblade.fandom.com/wiki/Ledios_Arms https://xenoblade.fandom.com/wiki/Ledios_Cuisses https://xenoblade.fandom.com/wiki/Rex_Greaves
It's a mixture of quest exclusive enemies (especially bad for the Ledios Arms) and other stuff you probably don't fight much. Compare to any of the Lancelot armour's lists: https://xenoblade.fandom.com/wiki/Lancelot_Gear or https://xenoblade.fandom.com/wiki/Lancelot_Armour
You don't need them but they can help a lot. You definitely need some improvements to your accuracy if you are using a physical team, but there are many options for that. Night Vision + Agility gems are just some of the more efficient options.
You can get Agility V crystals from the Ether Mine once you have level 5 special in colony 6 You can trade Scarlen at Satorl Marsh for rank V Night Vision gems (generally good enough, about 40% increase). Rank V cylinders are exclusively dropped by Ancient Daedala.
Other options for improving your hit rate are to skill link permanent agility bonuses (Melia and Sharla have them) or just temporary ones like % bonus for first 30 seconds, or increased agility below half health. Some skills increase accuracy directly like Bullseye. Most physical characters have an agility skill tree for +15 agility, though most have other even stronger passive tree effects you would likely rather have active. And finally high level arts get a hit rate bonus, 5% per art level, so if you aren't too concerned with auto attacks landing constantly (e.g. maybe for Reyn) you need way less agility to hit. I wouldn't usually recommend abandoning auto attacks, but it is helpful to remember your arts are much more accurate. Dunban also can run Serene Heart as an option, though it's not usually ideal.
For reference the superbosses have 50-120 agility but get up to +200 hit and avoid bonus on top from level, meaning you would need the equivalent of up to 300 agility to hit 100% reliably. For Abaasy it's 280, Belgazas it's 250, Arsene it's 300 (320 at level 98 or below) and for Daedala it's 200 (rising to 280 at level 95 or below). Between all the boosts to agility normally you can get to around 170+ agility out of battle fairly easily, and when you stack up things like night vision and other in battle agility bonuses, it's pretty easy to reach 250+ hit, often more.
Ether teams can just bypass all of this. All they need is the Enlightenment skill linked and their ether attacks should be 100% reliable, provided their arts levels are high.
Also a topple lock team doesn't need anywhere near as much accuracy. Enough to land the first few arts to break, and that's about it.