Yes, but not nearly so many as the wizard.
In play I don't agree.
Wizard are complex to build with an overwhelming number of spells, but in combat they are usually pretty straightforward and easy to execute. Obviously that depends on the spell and the character, but generally I think it is not hard. Fighter subclass abilities are quite complex and figuring what to use when can be quite complex. Specifically the "Knights" - Eldritch Knights, Echo Knights and Rune Knights are very complex in combat. While these subclasses may not have as many "things" to count as Wizard spells they are complex in execution, particuarly when combined with class mechanics that tend to promote attacking with a weapon.
Using Eldritch Knight as an example because it is easy to compare to a Wizard - They have the same spells as a Wizard but far fewer spells they can cast and far fewer slots than a Wizard of the same level. Despite the smaller number of spells, the actual play of the character in combat is generally more complex than the Wizard.
Choosing which to use and when to use them and/or their class abilities is very complicated - Extra Attack or Blade Ward and War Magic ..... or Green Flame Blade and War Magic .... or ready a spell? Action economy and concentration concerns go into the decision and are far more complex for the fighter than for the Wizard even though the spells are the same and the fighter has fewer of them.
I am DMing a campaign right now and the party is a Psi Fighter 8-Order Cleric 1, Giant Barbarian 6-Rune Knight Fighter 3, Rogue Thief and Wild Magic Sorcerer. They are level 9 right now. The players playing the Sorc and Rogue are newish (they played BG3 and wanted to try the real thing).
The Sorc is by far the simplest of those in combat and has the shortest turns. She has a few go-to spells; fireball, magic missile, Storm Sphere and Poison Spray. Most of the "mistakes" she makes are things like poison spray on a Zombie or Fireball on a bunch of Devils, but her play is extremely straightforward. The only thing she gets "stuck" on is converting SP to spells.
The Rogue is a little more complicated, mostly things like should I steady aim and use my longbow (Elf) or run up and dual wield with my vorpal scimitar and sunblade (she also has mobile).
The "mostly" Fighter and Barbarian-Fighter are by far the most complicated in play (and have the two experienced players playing them).