After all, if the contractor had some strange anomaly where he pays 100% of his income in tax, why would that matter to you?
Do it yourself: Miss out on that hours worth of salary
Subcontract: 2 times tax is paid.
Obviously this has implications on negotiation. This is exactly the reason why services are considered very expensive in the Nordics (as in 80USD to get your hair cut).
Note that this needs to be compared with a company getting their stuff fixed. Their contractor costs are fully deducted from their income.
In my example, a contractor who's twice as fast needs to cost $76 or less per hour . Thrice as fast is $114 or less.
You're right in principle though, just not on that calculation. In Sweden we have tax deductions for private citizens exactly to combat this issue: up to a certain amount per year can be deducted from your income, just like a company can, for certain services (such as cleaning or house repairs).