While evaluating Veeam Backup and Recovery to replace Azure Backup Server for VM backups, we have just run into this issue.
We'd like to recover files from our file server VM backups (created with VeeamB&R), but the D: drive in the VM is a Storage Spaces volume. This was done deliberately to get around the limitation in Azure Site Recovery that requires disks (.VHD/.VHDX) in replicated VMs to be no larger than 1TB. Yes, we replicate this VM to Azure Site Recovery for DR purposes, as well as back it up with Veeam.
Veeam has made a point of stating that Microsoft says Storage Spaces aren't supported in VMs, but they are supported in Azure VMs. That contradiction hurts my head...but as Veeam doesn't support FLR from Storage Spaces volumes, it looks like VBR won't fit our needs and we'll have to look elsewhere.
Starting up a copy of the VM just to get a file out is cumbersome and slow; a pain down and round the back as someone already said.