Impact of keeping 100+ Linked Server Objects open in MS SQL Server
Solution 1:
Linked servers were a drain on resource, particularly RAM, in the 32bit days - hopefully you've moved on from those days. I think your proposed solution would work, and the "pain" would be at the centralised SQL Server end.
However, linked servers can be a bit problematic sometimes - have you thought about using powershell/vbscript/SMO scripts to query these instances, and then load the data into that centralised SQL Server?