You get "Not your keys, not your crypto." There are other benefits to keeping your assets on-chain in a wallet that newer crypto investors may not be aware of.

Airdrops

Simply put, airdrops are the distribution of an amount of a native token to all holders for free. A variant is one that involves you engaging with social media to receive the airdrop, but for our purposes we're talking about the no-effort gain that comes from simply holding the token in a wallet. Airdrops typically (but not always) occur relatively early in the project's life cycle in an effort to spread awareness and buzz.

Perhaps the recent "gold standard" example of an airdrop that worked out well for holders is Uniswap. They decided to airdrop 400 UNI tokens to all Eth addresses who called the Uniswap v1 or v2 contracts before September 2020. This was worth $1400 USD at the time, $2544 right now (it was worth $17,600 USD at All Time High.)

Automatically accumulating tokens and reflections

I personally have a small amount of one of this sub's favourite punching bags, VET. It was only when I moved it to a wallet that I noticed it automatically accumulated the chain's gas token VTHO, albeit at a tiny fraction of the chump-change amount of VET I hold (0.00000005 VTHO per one VET per day.) Not exactly retire early money, but holding VET (or any other crypto with a similar mechanic) on most exchanges does not generate this passive "income" for you. Similarly with reflections or taxed tokens where a percentage of transactions is automatically redistributed to all holders.

I get that it's a feature commonly associated with shitcoins, but it's very back-brain limbic system-satisfying to watch these token balances grow in my wallet. As with airdrops, on an exchange this is typically turned off as "your" accumulating crypto is going back to them and you never see it.

As I note, some exchanges will be better than others. For Bitcoin maxis, neither of these factors will ever be relevant and I respect that too. If you're into any alts where either might factor in (admittedly airdrops can arrive without warning or never) well I'm not your real Crypto Dad but I'd suggest it's worth considering moving your assets off exchange to take advantage of these on-chain features.

There'll be other perhaps more subtle ones in play too, let me know what I've missed ????