Using my own laptop for work currently, only have one piece of bespoke software which uses a physical licence key so no issues downloading it myself and using the work license. Access to the file servers is via Sophos VPN, so I tend to just log in, copy the files I need over to the company SharePoint drive so I can access it with OneDrive. Already had all the Office 365 apps downloaded.
I would not, however, have my company granted any sort of access to my personal computer. I'd have no objection to the systems being changed, but I'd then require a work provided laptop to do the job.
My other half is working on a similar sort of way, but their setup is remoting into the work system via a web interface, so absolutely nothing downloaded onto the PC with the work system running in its own bubble.