Hello Viswa,
If my understanding is correct you have a static route in every device in your network pointing toward the edge router, if that's so you can safely remove the static route on the edge router but please do so under a maintenance window in case you faced an outage and you need to roll back.
What I believe is happening is this:
1- In normal cases "both ISPs are up", you have two static default routes pointing toward both ISPs, your traffic is load shared between your ISPs, you are not using the BGP default routes.
2- In case of a failure in either ISP, your router continues to use the static default routes, unaware of the failure, even though one of your ISPs is down causing some of your traffic to get dropped. In a previous post you said removing the route map or the as-path access list solves the problem, this is because now you are getting the full BGP table, and your router does not need to use the default route because a more specific route already exists, that is why the problem gets solved.
To solve this problem, I suggest using the BGP default route instead you can do so by removing the static default routes.
As for your second question, about using OSPF to distribute a default route to the rest of the domain to replace the static route toward the edge router, Yes, you can do so, for that I suggest using this command under the OSPF config of the edge router.
default-information originate
for example:
edge-router(config)#router ospf 1
edge-router(config)#default-information originate
This command would generate a default route to the rest of the domain with one condition, you already have a default route in the routing table by other means like a BGP default route, so for example if you lost your connection to both your ISPs you would no longer have a default route in your routing table, at that time OSPF would stop advertising the default route to the rest of the domain.
When your connection to either ISP is recovered a default route appears again in the edge router and OSPF start to readvertise the default route again.
All the best!
