They may have some personal significance to Batman, but the main reason for it, both in and out of universe, is to set up a distance between Batman and anyone that sees Bruce. As in any Batman medium, Bruce is a playboy. So filthy rich it's a joke. Extravagant. Expected to be odd and eccentric, as rich people are known to be. It's explicit in how Vale and Knox talk about Bruce. It's how people talk about Clooney's, Bale's, even West's Bruce. West had abnormal tastes. Clooney had the garage. Bale burned down his house at a party. Followed by their very carefree use of money. Clooney's donation to the Circus, Bale's purchase of a restaurant to get a seat, and Keaton's generosity in opening cases of wines and giving Knox a grant...
It's all part of the act, the facade of Bruce Wayne.
From the 5th draft script essentially what was in the final:
And here we are in the arsenal.
On the wall hang EXOTIC WEAPONS. Every arcane implement
of death the human mind has ever devised. Knox lets out
a low whistle.
Look at this stuff. Who is this
Bruce ENTERS and stands just behind them. Vicki sees
him, but having seen him earlier, regards him casually,
like another partygoer. Bruce listens with interest.
Strange. He gives to humanitarian
causes... And collects all this...
Probably does it to get chicks.
They like him for his big charity
I think it's his enormous...
bankroll they go for.
Hey, the more they've got, the
less they're worth.
This guy must be the most worthless
man in America.
Oh yes... thanks. Oh, Alfred,
they need mare wine in the front
and someone named Mrs. Daly wanted
a copy of the menu. Oh, and,
Alfred. Give Mr. Knox a grant.
He winks at Knox. And goes the OTHER way out of the
roam. Alfred fluidly sweeps up Bruce's glass and follows
him briskly OUT OF THE ROOM. Knox is stung and Vicki
Nice talkin' to ya, Bruce. Now
are the rich odd? Yes they are.
Sorry, I was -- He's comp-lic-ated.
I said odd.
Ah -- Well you're not the only fan.
This guy loves himself. There're
mirrors in every roam.
And indeed, the two of them are standing before an
enormous WALL MIRROR, eight feet wide, running from
floor to ceiling.
Maybe it should be Bruce VAIN.
Batman is pretending and faking as needed to keep them thinking of him as he wants them to think.
Batman is also prone to collecting. He keeps trophies of everything he does. His cave is full of weapons and devices meant to kill him. The Penny, the Dinosaur, etc. All of his different suits, and the suits of his robins, in a case, on display. You could say it's an orphan or neglected single child's obsession with filling a hole in their heart with stuff...