It shouldn't be unusual for a character to want to use their proficiencies more. The frequency of Arcana checks are mostly in the hands of the player with minor sway from the DM. They decide the DC, but the rules already defined the check.That logic works when you're making a lot of checks. But you can't assume it will all average out in a scenario that comes up maybe once every two sessions. "Arcane mystery" is not a particularly common occurrence.
Moreover, the wizard's likelihood to roll highest shrinks dramatically when you consider there are 3-4 other PCs. In a party of 5, even if the wizard has +9 and everyone else has -1, there is close to a 30% chance that someone else beats the wizard's roll.
When these unusual scenarios come up, they should be a chance for the relevant PC to step up and be awesome, not for them to fall on their face and look incompetent because they blew a roll.
A wizard with Arcana proficiency should be attempting to recall the lore of most magical occurrences. If they approach a rune, arcana. A Magic Item? Arcana. A summoned creature? Arcana. A magical effect? Arcana.
And its not just the obvious stuff like their names and features. Its also the lore and history behind the target. Information which may either completely change the party's plan, or just be fun tidbits of knowledge.
My point is that characters should be asking for their checks when they see the opportunity so that the game may progress using both their abilities and their ability to lean into what makes their character special.