Best/worst is subjective. More/less useful is less subjective. Roy has to be used every chapter. Eliwood doesn't. Ergo Roy is more useful than Eliwood. Eliwood could have made up for it with battle prowess, but unfortunately he's decisively below average, partly because of his late promotion. After promotion, he has nothing going for him. His movement is worse than a paladin and he starts with an E in lances.
Eliwood promotes Chapter 26 in Hector's Story. He has around ~8 Chapters of leveling and active contribution, which is pretty good considering most of those maps are swarming with enemies. He also doesn't get an E rank in lances but rather a D rank, which is significant because allows javelin usage (aka 2nd best lance in the game).
He might have 1 less move than other Paladins but he's still on a horse, so has canto, and can participate in rescue and trade chains that unmounted units just can't participate in.
Eliwood has shit bases but his growths are actually pretty OK. The problem is that they're not crazily offense slanted like, say, Hector's insane 60% strength growth so you get people often basing his combat performance on empirical evidence. Its very easy for him to reach the magic 14 attack speed required to double basically every mook in the game because enemy units are bad in this game. He's not a combat powerhouse but if you choose to give him the first Heaven Seal, he has plenty of utility and he really isn't any worse than the other Paladins you use not named Sain (and Marcus I guess).
Note that I'm not saying Eliwood is GOOD. He isn't good, since the Heaven Seal is worth $$$$$$ and neither Lyn or Eliwood are worth more than Killer Lances, but he's perfectly usable in both utility and combat purposes if you want to use him.
As for Roy? The basis of your entire argument is that the Binding Blade is good, ignoring that its a 20 use sword that does little but serve as a crutch for an underleveled Roy for the last two serious chapters of the game, and he's an "active unit" because he's force deployed and has capture thrones every map. But outside seizing the throne what can Roy actually do? Roy can never get a horse, he can't hit hard enough to put a dent into axe wielding fighters and is actually at serious risk of death, he gets murdered by the Nomads on the Sacae route, has WTD against Pegasus Knights on the Ilia route which already hampers his already weak offense and defense, and has to be placed far away from enemy Purge/Bolting users because guys like Ohtz hit so damn hard. His serious utility contributions basically start and end on Chapter 4 where his rapier is useful for finishing off stupid number of cavaliers that Marcus leaves on low HP. He's a liability for the majority of the game and his forced participation never has him actively participating in anything.
The comparison to Ike was very deliberate. If Roy being FedExed to the throne is a validation of his worth, and the criteria that puts him ahead of Eliwood who isn't even the worst lord in his game (that's Lyn), then he's definitely better than Path of Radiance Ike because map conditions don't necessitate the "use" of Ike every map and Ike is pretty bad at combat until he gets Ragnell (bad bases, sword locked, passive enemy phase, low movement, no canto, doesn't get overpowered weapon that makes him combat viable until the second last chapter of the game hey doesn't Ike look like Roy). I've sperged here but your argument really makes no sense unless we're giving units disproportionate value for doing a task that they didn't really assist in.
