It's still a math problem in the end.
Today if you want to break into someones encrypted data, you either have to break encryption algorithm (which is hard and by hard I mean even stuff we consider insecure like 3ple DES are still not broken) or you have to break each data individually.
With skeleton keys that changes. Suddenly all the world secrets are one* key away. That is the big difference. Doesn't matter how you do it, it fundamentally changes the equation
And you open up HUGE attack vector, by enabling bad actors to bribe/coerce people with access to skeleton keys.
* Doesn't matter if you split it up, have different org have parts of keys etc.
During usage, all pieces of master key will have to be brought together into one place (phisical or virtual), so eventually still only one breach is needed.
If I encypt data using encryption without backdoor, then to illegitimately get clear text requires effort X, and it gives access to 1 persons data. If whole country encrypts data using backdoored scheme, then effort Y will give access to data of 100 000 000 people. It would seem that security of the backdoor should be 100mil times stronger then that of usual crypto.
When discussing encryption, many people say that this is an impossible problem to solve because of math. This conversation has shifted to being a problem about incentives. Math is impossible to change. Incentives are changeable. If the only problems here are the specifics of the scheme and the incentives of people involved, those are solvable.
>Problem as stated is, that if skeleton keys are broken, then everything everywhere gets broken.
Which is why you build redundancy into the system that would require multiple independent breaches and a system to reencrypt data in the event of a breach.