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I'll have a conversation with my DM and see if they feel the same way, possibly suggesting that an additional save when the creature takes damage would bring it back into line with the other spells.

Edit: Followup

I discussed Fear with my DM and, after seeing this comparison, he agreed that its single-save possibilities were out of line with other spells at the midlevel. Going forward we're going to house-rule Fear to also allow a save when the target takes damage.

Level 1: Charm Person, Color Spray, Grease, Sleep, and Tasha's Hideous Laughter

Grease and Tasha's Hideous laughter both allow a save each turn to escape their effects, and failing that save is going to make it difficult to function in combat. Also they both use up the wizard's concentration. These are prototypical 5e save or suck spells and this type is still common at higher levels.

Charm Person is the odd man out at this level. It is very limited; the creature must be a humanoid and they have advantage if you're already in combat with them. That said if they fail the save you have up to an hour (assuming concentration) to do anything except attack them.

Special Note: Concentration

Nearly all of the these spells use up a wizards concentration. The four exceptions are Color Spray (which only lasts one round), Grease, Sleep, and Blindness/Deafness. Since concentration is near-universal to save or suck I won't be mentioning it again in the comparison unless it's an unusually long case.

Level 1: Charm Person, Color Spray, Grease, Sleep, and Tasha's Hideous Laughter

Grease and Tasha's Hideous laughter both allow a save each turn to escape and failing that save is going to make it difficult to function in combat. These are prototypical 5e save or suck spells and this type is still common at higher levels.

Charm Person is the odd man out at this level. It is very limited; the creature must be a humanoid and they have advantage if you're already in combat with them. That said if they fail the save you have up to an hour to do anything except attack them.

Conclusion: Fear is... actually quite unique

Looking through this list we see that Fear is the only spell before level 5 that only allows one save and lets you still wail away on the target. It's versatile in that it allows no extra advantage if used in combat, and it's not limited to any class of creature. It is situational though, if they can't run then they can resort to ranged attacks and still function. And if they can run you need a way to keep up with them. All that said, and looking at the other spells around at the mid levels, I'm convinced Fear's single save option is out of line with other spells at this level.

Conclusion: Fear is... actually unique

Looking through this list we see that Fear is the only spell (in levels 1 to 5) that only allows one save and lets you still wail away on the target. It's versatile in that it allows no extra advantage if used in combat, and it's not limited to any class of creature. It is situational though, if they can't run then they can resort to ranged attacks and still function. And if they can run you need a way to keep up with them. All that said, and looking at the other spells around at the mid levels, I'm convinced Fear's single save option is out of line with other spells at this level.