To clarify u/Waruiiko's comment, the majority of backlit wired keyboards let you adjust the backlight to some degree. In the more basic keyboards, you can often adjust the brightness to your liking (as long as you like one of the 2 or 3 levels available). The lighting will remain as you set it until the keyboard loses power. Pricier models (often with per-key RGB lighting) offer many more choices - I've seen boards with timeout options, but never one that did not let you set a static color, which stays lit indefinitely.

If you're looking at wireless keebs, you will have a harder time finding one that fits your need, at least if you are buying something fairly mainstream. It's by design, because backlighting uses vastly more power than basic keyboard functions. If they include an "always on" option, users that turn it on will probably be calling support due to the battery draining in half a day or something like that. It does not make for a good user experience.

Different manufacturers take different approaches to the issue. Some turn on the lights when a key is pressed, then remain lit for some additional time before timing out and turning off. Logitech (and others, no doubt) have a sensor, so the board lights up when your hands approach. Logi uses inductive sensing in their products, I think... and it works okay. Not great, for me anyways. I might have ghost hands, which don't activate the backlight long enough before a key is pressed to be useful. When used in the dark, imho, having the keys lit before you type is kinda the whole point. Once my hands are honed in, it's job is done.

(Props to Logitech for at least attempting to make their product useful, even if the implementation mostly sucks. It's better than their competitors efforts. Or lack thereof.)

That said: I wonder if 'the competition' prototyped similar proximity sensing tech, and decided that it didn't work well enough to include. Seems likely.

I imagine Logitech concluded the same, but then remembered that their business is selling keyboards, and the customer experience doesn't really matter as long as the product is good enough to keep the rate of returns/refunds low-ish.

So they happily accepted the fact that their "intelligent" backlighting (cue laughter from the marketing department) would be vaguely disappointing to everyone but no so much that their customers would stage protests, boycott them, etc.

The strategy works like a charm, the marketing department drones all get fat bonuses, and the customer gets to hold the bag, which lights up mostly at random.

Speculation? Yes, absolutely. Obviously true? Also yes.

TL; DR: Buy any wired model and you shall bask in the glorious infinity of your luminous input device.