Regardless of whether it is arbitrary or not, regardless of whether it fixes a great injustice or not, the question I have is whether, assuming the house rule is in place, the game would be worse. I've run into games with house rules I considered unnecessary and arbitrary but which didn't affect my game enjoyment, as I saw them as neutral changes rather than negative ones. Is there anything about the OP house rule in your eyes that makes it actually negative, rather than merely unnecessary?
As to your last point, remember this is spellcaster vs. spellcaster, so reducing the effect of one spell to make another type of spell less likely to fail doesn't change that, either way, spellcasters rule the world in D&D.
First off, neither you nor Jimlock presented any a compelling argument that protecting illusions from DM
improves the game. What you've done is argue that the world should work the way you think it should. That' doesn't make the game fundamentally better. That just changes it.
Second, deciding that Detect
Magic can't detect the inherent magic in an illusion spell, undermines a basic tenement of D&D reality. Magic is a primeval force in the D&D world. It's as strong and as prevalent as gravity. Dropping Detect Magic down to a 0 level spell is an indication that the first thing a caster should be able to do is learn how to recognize magic when it's being employed. Illusions are still magic. Nothing you or anyone else has said challenges that notion or suggests otherwise. Ergo, the ability Detect Magic must work when an illusion is present.
Third, you've asked how it harms the game? It disrupts the logic of both DM and Illusion spells. You've arbitrarily decided something should work differently and you've got no justification that makes any sense other than you want illusion spells to be more effective. Well, I want Monks to be more effective. What's the harm in making the Monk the most powerful class? The simple answer is illusion spells were not meant to be as effective as you've decided they should be. The complex answer is that your change most assuredly throws a whole lot of things out of whack, the majority of which you won't see until it's too late (no pun intended). Undoubtedly, you're going to view those changes with a bias filter and not view them objectively.
Fourth, you haven't made any compelling case that illusions are in need of this change. I'm going to repeat what I already said and what lots of other posters have said through examples: Illusions can still be employed with tremendous effect. Tremendous. Judiciously placed and employed with artful skill, a party would never suspect an illusion to begin with.
Fifth, if you remove DM's ability to detect the illusion, you take away a very useful way for you to control the party's actions. In some cases you WANT the party to suspect an illusion and waste time trying to detect it. Particularly in combat. If the party knows DM will not detect illusions, then they won't even try. In effect, you claim to be using an illusion, but it might as well be a real construct because the party may have no way to know otherwise.
Sixth, I hate to say this, but this whole line of reasoning smacks of a gamemaster whose clever illusion spell got foiled by a simple DM and now you guys are upset. At the risk of sounding rude, if the party is consistently using DM to find your illusions, then you aren't doing it right. It's not like the gamemaster is under some sort of monetary restriction when creating campaigns. As I said with my first point, I don't see anything that justifies your change other than whim. Change without real justification isn't good, it's bad because the presumption is that the game rules were tested as is and more often than not strike the best balance for playability.