Due to the company policies I have to use these machines.
That will likely not change and you will not get an exception. In any country with data protection laws, whether it's Europe with its GDPR or other countries with their respective laws, it's a legal nightmare for companies to give data to their employees outside of a restricted work environment.
The difference between a virtual machine you "dial into" and working on your own PC is that one is "secure" while the other is not. Sure, you could maliciously copy data from either, but if we assume that you are being a model employee and your company is being a model company, there is near zero risk for data to leak on the VM while your personal computers are a huge risk to the company. Your computer could get stolen, you could sell it for a better model and someone recovers the data on the drive, anybody in your home as a guest could take a peek while you are unaware, or it might simply contain viruses.
So allowing you to use your own computers for work is just not going to happen if you work for a company that wants to remain legal in a country with data protection laws.
So what now?
Do what you would do with any topic that hinders you to work effectively: gather data, present it, and suggest a solution.
For example, if your tool takes too long to open, make a note of it, sum it up and bring it to your boss. Probably informal first: "Hey boss, I noticed $software takes a long time to open our files. I was curious and measured it. This week alone I spent 3.5 hours on waiting in front of the loading screen. Do you think we could improve this? I'd rather spent the time working than waiting."
The important part is to have data. Every computer user ever thought their tool "takes too long". So bosses are used to people saying that and will just ignore it. Bring them data. Show them how much they are actually losing. Bring them enough data so they can measure your lost time (= money they paid for nothing) against the cost of giving you what you need. A $5000 upgrade sounds expensive when you say "but my machine is so slow", but it sounds dirt cheap if you say "I'm losing $500 of productivity a week".
Make it easy for deciders to see the problem and fix the problem and they will.