I remember back in the 90s/2000s, it was common for download sites like cnet or tucows to have you click a link and there would be a big 5 second timer and then the download would start and there was always a tiny link below that you could use to start the download manually in case the timer didn’t work. Nowadays, I can’t recall having seen one of those in years.
Was it a technical limitation? An advertising thing? I don’t recall ever seeing ads on the download page although I can’t recall if I had installed an adblocker by then.
Are you talking an explicit timer, or just something saying that “if the download doesn’t start in 5 seconds, click here”? The latter wasn’t actually a timer, but just waiting on the system to communicate with the servers and decide which one to download from based on which connection was fastest and which server was available. Doing so could take a few seconds. These days, this sort of thing is often handled better behind the scenes, and so the time needed to do so is too short to notice.
If you actually mean explicit timers, then those still exist today on sites that are both smaller and have a lot more downloads. They mostly exist for two reasons: to discourage just willy-nilly downloading (which wastes bandwidth), and (more often today) to funnel people into paying for a subscription.
Wasn’t it usually, “You must wait ten seconds for the download to begin (or buy our product and get instantaneous downloads and never have to wait again!!)”
They’re trying to get you to pay for something better.
If they set the page to download the file immediately, it might be competing for bandwidth with assets on the page - including the ads, which might not load completely and may not register an impression, but also other parts of the page, so the page might look like it was broken, scripts might not run, etc.
Less of a problem with modern browsers and internet connections.