Once a 2nd major exchange enables LN deposits & withdrawals, all of them will be essentially forced to do it so as not to lose out in the arbitrage battle.
Arbitrage is actually really an excellent point -
this could perhaps even be Lightning's killer app, as payments in BTC (be it per LN or not) are still not too popular, but the speculation business with BTC is thriving as never. And it would offer real added value for arbitrageurs.
I believe when Taproot is activated, helping obfuscate the opening of channels, a Lightning privacy-app might be THE killer-app the community is looking for in my opinion.