In general about armor in 5e; Both medium and heavy armor exists at various price points from cheap to expensive, of course AC increases with price. (Lae'zel's half plate is actually a top-tier medium armor that should cost 900 GP, weird for a 1st level character to have)
Typically heavy armor users will have 1 better AC than a medium armor user with same tier gear, that's nice but not a huge advantage. The main benefit of heavy armor is that it doesn't require any investment in DEX, so you have more points for other attributes.
Yeah but also STR armour requires high STR right? So you get to dump DEX, but you need high STR instead.
And DEX saves tend to be more important than STR saves I think
There's a movement speed penalty for not satisfying the STR requirement of your armor, but it rarely matters much. A caster in heavy armor will usually have no problem getting in range to use his spells even if he's a bit slow, while a melee character is going to be focusing on STR anyway.
It's true that DEX is useful for saves an initiative rolls, but the difference between say DEX 8 and DEX 14 is only +3, so in both cases it mostly comes down to the luck of the D20, you won't notice that much difference from having shit DEX.