There are two typical scenarios when people carry default route in dynamic routing protocol, I'll address these separately and explain why you shouldn't do it, and what you should do instead.
CE (eBGP) PE
This is probably the most common scenario, maybe you're giving your customer default route, maybe it's your own firewall or really any situation where neighbor won't carry full routing table and neighbor isn't strictly same administrative domain.
Problem with default route here is, that if your PE gets disconnected from core, you're still originating the default route and CE is unaware of this and you're blackholing customer traffic until BGP is manually shutdown. You could conditionally advertise default, but that is just useless overhead, instead of default you should advertise to CE any aggregate route which is originated from multiple core boxes, such as your PA aggregate, or really any stable route originated from multiple places, but not local PE.
Customer would just add this to their router:
Slight cosmetic complain is that if you add interface to the static route, IOS disables recursion, so you cannot enforce that the static route will disappear if next hop does not recurse behind that one interface. But it is purely cosmetic, as functionality will remain regardless if 192.0.2.0/24 will continue to exist or completely disappear. If it will continue to exist, customer will just need to local-pref/med 192.0.2.0/24 to have expected backup default selection.
PE router without full table
Typical solution is to have two RR iBGP peers to originate default route. This has the problem that RR probably aren't always in optimal forwarding path, especially in single fault, but in many cases never. So you'd stop iBGP from originating default, and you'd instead add this to every router having full bgp view:
Exception that proves the rule
If the end device does not support recursing routes, then obviously this won't work. And there still are such devices, though it's unsure if you want to be routing in such devices to begin with