You can just minimize the browser or have it running in a different browser tab and just ignore it.
I see what you're saying, it would be cool to have it in the tray, running as a task.
I'm heavy in the belief that web applications will be the future of nearly all applications. I've always geared TestMy.net toward a 100% browser experience.
The new version of TestMy.net is a full PWA. Taking advantage of many new browser features, 100% adopted by all major browsers at this point. In the next versions of Chrome you will be able to install TestMy.net and have it run and behave as a normal desktop application. You can also add it to your mobile device and have a more app like feel. It's much faster and offers offline capabilities. For instance enabling auto resume for the automatic speed test, a feature I've always been looking to add.
Testing time is near.
The new functionality coming to developers in browsers ... is blurring the lines between native and web applications. I imagine it's only the beginning. The progression at the browser level is ramping up quickly. Browsers are implementing cutting edge features at an astonishing rate and it's feeling like ALL of them are agreeing to standards for once. I've been developing for the internet since the beginning, never seen this kind of progress.
I've never developed for iOS, Android, Desktop etc. Now and especially in the future ONE web application can branch across all of those platforms. Especially when you're a single developer... it can be hard to manage even 1 code base.
So I hope that in the future it's just part of the way TestMy.net works... using the latest tools I have available.
Hopefully you'll see by minimizing it... you can run it that way for over a year.