The bind weapon thing is useful for more than just thrown weapons, though there is a build that uses it for just that. It is also handy when enemies disarm or heat metal you. For example, the commander of the Githyanki patrols likes to disarm. So then suddenly your 2h weapon specialist has to waste a turn picking and up and equipping their weapon, or be a laughable excuse for a monk or ranged attacker.
Spell-wise, they do get some handy spells. Longstrider and Misty Step both let them improve their mobility. Shield you mentioned. At level 8, they can get Hold Person or Blur, as at that level, they get access to the whole Wizzy list (for level 1 and 2). When they are given the option to swap out a spell, they can also choose a replacement from the fully wizzy list.
They are also half casters, which means some of their levels count toward your caster level (which impacts what spell levels you gain access to). So say you wanted to make a fighter/wizard with 6 levels in each class. If you took either of the other two fighter subclasses, you would not have access to any 4th level wizzy spells. But if you take Eldritch Knight, you would get 2. Now say you wanted 8 levels of fighter, and 4 wizzy, instead (or 9/3, but that's a bad split). The Eldritch Knight version would be able to cast 3 fireballs. The others would not be able to cast a single one. And you can drop that fireball right on your allies, because you'll be an evocation Wizzy. Or, instead of fireball, you can forego int, and cast haste on yourself instead. If you go 10/2, you'll only have 2 3rd level spells, but you will then be able to hit an enemy, then cast a spell on them with them at a disadvantage.
But basically, you are either doing it for the mobility, or you want to MC in a little bit of something else. Probably wizzy.
Good points. I have 2 corrections/points of concern.
1: Technically they are 1/3 casters not 1/2. Paladin and Ranger are 1/2 casters, and their spells progress faster than Eldritch Knight and Arcane Trickster.
2: While hold person is a good spell, it DOES require the target to make a save, so if your Intelligence score is low, they'll resist it a lot more. I would suggest Misty Step and Mirror Image or Darkness or Knock/Arcane Lock. Something that adds utility without being dependent on your Int score. Darkness can be especially potent late game, if you have any of the multiple gear items that prevent you from being blinded. This will give you advantage against enemies in your darkness, and prevent enemy archers and spell casters from targeting you.
Re: Multiclassing. I would point out, that fighters get a 3rd attack at level 11. So, if you take more than 1 level of another class you're giving up 1/3 of your damage output at higher levels. IMO, there are better ways to get haste than casting it yourself, and if you MC you also miss out on the 12 level ASI/Feat. I think the EK is built well enough to play as a straight class fighter, but I guess if you can't live without the spell sword fantasy, you CAN dip wizard. Just be sure to not neglect your Int stat or your spells will be resisted most of the time.
