The reaction would probably be better than "I didn't know I forgot to lock the door" or "I knew I forgot to lock the door, but was too lazy to go home and so I hoped for the best."

Plus, locks are trivially pickable, so it's not like they stop someone that wants to break into your house from breaking into your house.

Locks are not trivially pickable. It only looks that way if you watch a skilled person do it. It's much harder than many impressive juggling tricks, for example. Smashing in a window, now that's trivial.

Neither matters though, because a big purpose of locks is to show that you took reasonable precautions in order for your insurance to be valid. (YMMV, IANAL, etc. but that's the case here.)

I'm about as unskilled a lockpicker as you can get, and I can pick the four-pin locks on my apartment fairly easily. Someone with practice could do it even more easily.

(I've never used a pick gun, but I hear that makes it even easier. Especially for locks that don't have any particular anti-picking features, like the majority of locks on people's homes.)

In the U.S., there usually isn't any language in a homeowners policy about doors being locked, so if you have a police report, they don't say anything.

Ah, I didn't know that. That's one less issue for them to worry about.