Try harder
The cost of migration is the cost of migration. Any migration from any OS to any other OS costs money to evaluate the current environment, identify applications and systems and how they work, plan the migration/cosolidation/retirement of each one, audit server & workstation hardware, packaging, networking and VPN access, security and encryption, hardware upgrades and replacements, training and information, employee/company policy adherance checking, fire-fighting, licensing and help and assistance. That would be my general list for a windows to windows upgrade.
Regardless of the migration path, all these items are required; you can't get away with that (unless you want the project to waste money or fail.)
If the migration path was to Linux, all the same items apply. Except licensing costs for the Office suite, email/webmail, databases, antivirus, firewalling, caching/proxy, web servers, the OS, upgrades and applications. I don't even think you would pay any more for the technical people to do the work ether. Linux people in my experience, tend to be very understanding of the fundamentals of computing and how the systems work.
MS Office is not the be all and end-all. Open Office does a good job of office productivity and is only hamstrung by add ins/dlls/toolpaks which vendors may not supply for Linux/open Office. In these cases, either Citrix or MSTS or VirtualBox/VMWare is available, so I agree with you that it's not a like for like immediate swapout, but workarounds and compromises are available.
In parliamentary setting, Linux would be a reasonable choice but would be a tougher gig on a dealing floor where apps are often badly written, arcane and the bank hinges its entire P&L on ropey old apps.
Todays herecy always becomes tomorrows orthodoxy. It is only ever a marketing campaign away. All I'm suggesting is that it is worth keeping an open mind on the possibilities. Linux will probably be around in 50 years time. Windows probably not.