Theres no limits to cantrips you can use.
Spells are limited because they are a lot more powerful and you need to use them strategically.
I don't see why a wizard would become a 'backup archer' when they can cast unlimited bolt of fire or ray of frost.
Thanks.I have to admit that i'd not noticed those two spells were unlimited.
Still, can't help thinking mages are a little
hard done by in this build. That's just because you don't have familiarity with D&D. Low level wizards, this game included, are in a way better place than they used to be in previous editions. Cantrips are unlimited use and they do more damage than level 1 spells used to back in the day.
My advice is to just forget everything you know about mages from other games. While those games likely drew inspiration from D&D, they aren't D&D. You have all the tools you need to be successful with a wizard (or warlock) in this game. Understand that you aren't just mobile artillery like other games. Sleep and Grease make hard fights manageable and manageable fights easy so don't just slot all damage spells. Use all your tools.