From my perspective working as a network engineer for an ISP, the bandwidth issues are almost never on the server side. The vast majority are going to be either between the Datacenter and the user, or on the users end.
Depending on where the issue actually lies a VPN can definitely alleviate the issue.
From an insiders perspective you have a couple issues with ISP’s. Note there are almost certainly exceptions to this but from the 15 years I have working in Networking in the ISP space this is close to universal.
First no ISP has the backhaul to feed 100% of the bandwidth they are selling. There are formula’s we use to determine how much we need vs how much we sell. In many install cases we have as little as 20% of the backhaul. The theory is that at no point in time will every user be online and using 100% of their bandwidth. Different ISP’s have different policies on this, where I work the goal is that no link in our internal network ever sees usage over ~55% of capacity. Other ISP’s will gladly let those same links sit at 100%. As a note of interest around 50-60% of link capacity is where you start to see traffic queuing, which the end user will see as a latency spike. If this is the root of someone’s issue, the only fix is the ISP increasing their backhaul capacity in your area a VPN will not help.
2nd Many ISP’s have multiple upstream providers and traffic goes to whichever one the ISP’s BGP install has determined as the best path. This is a gross over simplification but BGP does not pick paths based on Link Speed, or Link utilization. BGP for the most part picks the path that crosses the least number of autonomous systems (essentially how many providers does this path cross). There are ways we can manipulate this, but it requires manual intervention, and changes to how our core installs routes to outside world. Sometimes a different path will be better for connections to a particular datacenter, even though it has a longer AS path. The Tier 2 (upstream providers) that your ISP ties into, also oversell their link capacity. A VPN may or may not help with issues here depending purely on where the problem link is. If the VPN traffic is still going to cross the same physical problem link the VPN will not help. If the VPN traffic bypasses the problem link the VPN could fix the issue.
These issues tend to be what leads into an ISP making a decision to throttle, or otherwise manage bandwidth. Every ISP has their own internal policies on this. Increasing capacity is very expensive, throttling and other bandwidth management techniques such as giving certain traffic higher or lower priority are far cheaper. If you live someplace, like large parts of the US, where there is only one provider there is almost no incentive to fix this. There can be a desire to wait until the current equipment is EOL (end of life) to perform any upgrades. VPN may or may not help with a situation where throttling is occurring. If the ISP is throttling all traffic to MS servers a VPN can help. If an ISP is throttling your connection specifically a VPN will not help. The last situation is not as common but I have seen it done, I have actually seen a contract for service with an ISP that stipulated that if your bandwidth consumption exceeded 75% of your subscribed bandwidth for more than 1 hour during peak usage times they would throttle you 20% of your subscribed bandwidth during peak times for a week.