The 'ink' (it's really toner) cartridges that come in new printers have a fraction of the levels in them as retail cartridges. They're referred to as 'starter kits' if you look in the small print. You're looking at a false comparison there.
That actually wasn't true when I bought a Canon MG6000-something. When the price of the printer went below the price of ink, I bought a second one and stuck it in the attic, which came in handy when the first one died. Both printers came with standard ink cartridges.
The HP laser printer I bought recently, on the other hand, did come with starter cartridges with a smaller amount of toner. My impression is that starter cartridges are more common with toner than ink.
It depends on the printer. I’ve had pretty good luck with brother laser printers coming with full toner cartridges in the past, although my understanding is on many modern models that isn’t the case anymore. You definitely have to read the fine print.
This is manufacturer specific. The Brother replacement cartridges are half the price of a new printer ($50/$100) and the replacements print ~3x the number of pages (2600) you get with the included cartridge.
Plus, the no-name toner cartridges work perfectly fine for Brother printers (I buy 2-4 per month for work). However, do not buy the non-brand drums, they are a waste of money; the genuine Brother drums last 4x longer.
You can get 3rd party toner cartridges for a fraction of the price of official cartridges. Just get the model # for the cartridges and look for a supplier on Amazon who seems reputable and where the product gets good reviews.
In my case, I've been buying 3rd party toner cartridges for my parents' Canon D300 laser printer/copier for years. First through one company I found on the internet years ago and then, when they closed up shop, I found another on Amazon -- I paid $20 for the cartridge I bought this past May (the official cartridge is about $109).