The use of HTTP compression is part of general web application performance to improve transfer rates and bandwidth utilization.
When you disable HTTP Compression it will have an impact on load times pages for initial page loads on first visit to the application each time. It shouldn't be too bad but maybe noticeable. The .js files will be a lot larger and therefore take just a bit more time to come from server to client and get loaded into dom.
Your trying to use a third party product to monitor our client side processing but you have to modify our default performance setting to do so. That doesn't sound like a great idea but if the data you get from Dynatrace is providing you some sort of good input then you need to determine if it's worth it. In my opinion a monitoring tool shouldn't have to disable performance settings to work.
The history behind this setting even being available was simply to allow for easier debugging of the scripting. When uncompressed it's easier to add break points, see true variable names, and step through the code etc. However, browser debuggers now allow you to click a button, aka tidy print, to uncompress the content so it's easier to debug. I haven't had to use this setting in many is years.