The issue in this edition is that spells scales by upcasting, instead by character level, so the attack spells quickly outdates. Then, as EK you can have use for Thunderwave for pushing. But at level 7 getting Shatter, is really worth to spend your action for 3d8 damage, instead doing your multi-attack?
The Eldritch Knight is a good subclass (in my opinion) but requires careful choice of spells.
As you say, basic attack spells are often less than your weapon damage. But there are still plenty of spells that supplement your fighting abilities or allow you to do things that you can't otherwise do.
Spells that deal area damage (like Shatter or, especially, the classic fireball) are actually not bad IF you can affect at least two creatures, because it'll probably be more overall damage than one turn of weapon attacks.
Shield spell is awesome but unfortunately requires a free-hand unless you have the Warcaster feat.
Then there are buffing spells like Enlarge/Reduce, Fly, Haste etc (ideally you will get a chance to cast it before combat begins so you don't use up your valuable first turn) and spells that can just take an opponent out of a fight completely like Hold Person.
Yep all utility and affecting spells are nice. My concern is with (damage) attack spells. I see much more valuable the cantrips than the spells, i.e. Chill Touch with the War Magic can be nice to prevent foe to heal, or Mind Sliver to apply a penalty so its weakens against your party casters, or even to yourself combined with Eldritch Strike + Action Surge (with the AS you use the Attack Action and with your normal Action you cast the spell) or casting the next round.
But pure damage attack spells, I think is a waste of those valuable prepared spells and spell slots of the EK as they combine with nothing of the subclass in any way and are directly outdated at the time you can cast them. Maybe a Fireball could do more damage than your multi-attack, but this one combined with War Magic probably makes better to get another spell for your list, as cannot change it like a Wizard at Long Rest.
The issue in this edition is that spells scales by upcasting, instead by character level, so the attack spells quickly outdates. Then, as EK you can have use for Thunderwave for pushing. But at level 7 getting Shatter, is really worth to spend your action for 3d8 damage, instead doing your multi-attack?
The Eldritch Knight is a good subclass (in my opinion) but requires careful choice of spells.
As you say, basic attack spells are often less than your weapon damage. But there are still plenty of spells that supplement your fighting abilities or allow you to do things that you can't otherwise do.
Spells that deal area damage (like Shatter or, especially, the classic fireball) are actually not bad IF you can affect at least two creatures, because it'll probably be more overall damage than one turn of weapon attacks.
Shield spell is awesome but unfortunately requires a free-hand unless you have the Warcaster feat.
Then there are buffing spells like Enlarge/Reduce, Fly, Haste etc (ideally you will get a chance to cast it before combat begins so you don't use up your valuable first turn) and spells that can just take an opponent out of a fight completely like Hold Person.
Yep all utility and affecting spells are nice. My concern is with (damage) attack spells. I see much more valuable the cantrips than the spells, i.e. Chill Touch with the War Magic can be nice to prevent foe to heal, or Mind Sliver to apply a penalty so its weakens against your party casters, or even to yourself combined with Eldritch Strike + Action Surge (with the AS you use the Attack Action and with your normal Action you cast the spell) or casting the next round.
But pure damage attack spells, I think is a waste of those valuable prepared spells and spell slots of the EK as they combine with nothing of the subclass in any way and are directly outdated at the time you can cast them. Maybe a Fireball could do more damage than your multi-attack, but this one combined with War Magic probably makes better to get another spell for your list, as cannot change it like a Wizard at Long Rest.