My "startpage" is a four-column list of stuff I usually browse. And usually I sit with my left hand at the left hand side of the keyboard, and with my hand on the mouse on the right. Doing CTRL+T then clicking on where I wanna go, is usually faster and less movements needed than having to manually type the one or two first letters.
I tried sometimes to put "widgets" or other things (like widget on a smartphone) but it's true what you say, it's an unwelcome distraction. But a couple of simple lists seems fine, for me.
That describes ChromeOS users of course, but there are Apple and Windows (and presumably Linux) users who have the same workflow.
RDP does exist of course as well as something like Guacamole so one is not limited to only terminals or web IDEs
Other than that, yeah, I usually CTRL+T and write right away.
Besides that, I don't use or care about anything on the "new tab" tab. Backgrounds, sounds, weather, news - that's all junk/noise to me. There seems to be no value for me in having them on the empty tab, when they're a click (or, in case of the weather, a glance on my phone or watch) away.
Just how it works for me, of course. Other's mileage may vary.
Sometimes I'll open a new tab and click the site I want from my commonly used sites Firefox presents to me on the new tab page. In such cases my hand is already on the mouse and two clicks is about the quickest I can get to one of those sites.
I can immediately redirect to any with 0-9 and still have quick access to the address bar via ctrl+k
The first question that pops into my head (being aware that this is a popular category of apps) is: when do people look at blank tabs? Whenever I open a new tab, it's with the intention of entering an address or a search term, and any content would be an unwelcome distraction.
I'd be more likely to use something like this if it lived under a regular domain name and I could put it into a pinned tab, personally.