The nominal burden of who "pays" employment-related taxes or benefits is completely separate from who the actual tax incidence falls on. Would you rather get paid $10k that you owe $1000 of taxes on, or get paid $9k with the $1k of taxes already withheld for you? Either way, the total cost of employing you remains the same for the company, and the take home pay after taxes remains the same.
Not quite, taxes are actually higher if you are self-employed. You have to pay SECA, which effectively includes the portion that your company would have paid otherwise (on top of the amount that they withhold and pay on your behalf).
That's not taxes being "actually higher", that's taxes being paid in a way that increases the total cost of hiring someone without showing up anywhere on the pay stub of full-time W2 employees. Like, it changes the numbers to something like "$9k with $1k withheld and $1k of employer taxes" vs "$11k with $1k of income taxes and $1k of 'employer' taxes that you now have to pay"