for a 2021 BMW 330i that's still under the 4-year/50,000-mile BMW warranty, you can definitely buy a BMW extended warranty. Based on what I learned last year, the price for a 7-year/100,000-mile BMW extended warranty with no deductible for the 330i will be around $2900 to $3200.(if you research this forum and find those BMW finance managers who will sell these plans at a discount)
Some people will say buying an extended warranty(even if it's from BMW itself) is a waste of money. That's not entirely wrong. An extended warranty, similar to insurance, is suppose to make money for the company or underwrite that offers it. They are counting on the fact that not all cars will have problems. Like a casino, the house ALWAYS wins.
Having said that, these plans offer peace of mind for BMW owners who keep their cars who keep their cars for 5, 6 or 7 years. The $3000 buys you protection for the extra 3 years. That's around $80 per month for 36 months. Without warranty, these items will cost way more than $3000 to repair/replace: engine, transmission, infotainment computer, climate control system, etc. Just one repair will offset the cost of the $3000 extended warranty.
An alternative is to NEVER buy extended warranty and put all that money away in an account for rainy day.(i.e. car repair)
I prefer to pay for peace of mind... but that's just me.
