The biggest cons of having your funds inside a cold wallet, in my opinion, is the fact you aren't going to make any passive income from it.
Not really. You can earn passive income by simply holding an asset that works as an inflation hedge.
Many people don't understand what making money is. Let's say you hold an expensive necklace. You can put it to work and make women pay for being able to wear it at events, but you'll be taking a risk.
You can also put it in a safe place and because fiat money is being created out of thin air, the necklace will grow in value anyway.
I hold my bitcoin offline and it's worth more with every halving.