In situations where evasion can be modified and it isn't just a matter of how often the word "miss" will show up in place of damage numbers, it usually refers to the number of invincibility frames you have and either extending the period of time you cannot take damage or the reverse. If not that, it may refer to the size of your hitbox decreasing, or the distance of which you can reach when performing some evasive action extending. No idea otherwise.
If I recall correctly luck can add to your general avoidability in FE. Since we have stat caps, a character that has 60% speed and 30% luck growth may end up being significantly harder to hit than one that has 90% speed growth and 0% luck growth. I also remember it not actually adding to one's critical rate in the GBA games.
I'm not weirded out per se, but yeah, I guess those stats often do exist--they may or may not apply, a lot of the times the advantages or disadvantages are minuscule enough that it doesn't matter much and you can go along with the same old equipment or attacks or whatever
Like, part of the problem is probably that most gamers are lazy and/or bad and don't spend a lot of time really delving into the details of a game's battle system or the like when it's not necessary. Like, it's much easier to just get some powerful equipment and keep using that instead of always adjusting and adapting.
Granted I think the latter is more challenging, rewarding, etc. and it's nice when game devs try to legitimately implement stats and resistances into their games instead of just making it kind of fluff or easily ignorable, but yeah, I do get where they're coming from in terms of not making that all mandatory and overwhelming more casual players... *sighs* it stinks in a sense—it's very difficult to appeal to all sorts of people at once—but whatcha gonna do
It's pretty hard to actually make these fluff stats highly relevant. You're either going to make some enemy ridiculously overpowered (like kirant's Void Giant example) by making them have no actual weakness or the enemy is going to have too many weaknesses to actually have a reason to care. Not to mention for balance purposes you're going to have to give a player the tools they need to actually deal with whatever comes at them.
Like for example, let's say that early on in a game, you encounter a generic Knight enemy. This enemy is very competent for the stage of the game you're at because you don't really have a huge number of options. They are resistant to physical, wind, slash and thrust attacks, and are not likely to be afflicted by bleed or stun status effects. However, this also leaves them vulnerable to magical, blunt, fire, water, earth, light, and dark attacks, particularly weak against lightning attacks, and still vulnerable to poison and slow.
Later on in the game, you meet the Knight's recolored super-cousin Magic Knight. Magic Knight is resistant against physical, magical, slash, thrust, and all of the elements...but still have a weakness to blunt damage and are easy to cripple through status effects.
In both cases they have their strengths and weaknesses but the Knight is so vulnerable the only particular reason they are going to be threatening is because you haven't reached the point in the game where you have a mage or a blunt weapon user (and you can probably just ignore the rest of the weaknesses anyway.) The Magic Knight however has a ton of resistances and the game needs to be designed for the player to be capable of actually exploiting the weaknesses it has left, which will either make them a cakewalk anyway or just an annoyance that asks you to change up your setup. (Or they just end up being a really overpowered enemy.)
Magic Knight is probably a decent enemy to include in a game like Fire Emblem (what with our inventory limits and resource management across a large team and everything) but it's going to be a headache for both the player and the game designer to find out how to make Magic Knight be an effective feature of the game in situations where your game mechanics focus on a small number of deployed units. Then there's the issue of how you would make several enemies like Magic Knight so that you can create diverse situations that won't be solved by just equipping the best set-up v.s. Magic Knight. Because if you don't...we're back to that point where all these fluff stats don't exist for any important reason (aside from maybe making the occasional overpowered enemy...though you don't need fluff stats for that either.)