[Da Bilge Troll]

Why must the hospital go through lot of legal expense to try to recover the unpaid bills?

For the same reason Mastercard has to go through lots of legal expenses to recover unpaid bills.

[entropy12]

You have very little sense of financial proportion.
A Mastercard has spending limits, typically 5 to 10K dollars.

A single hospital bill for a week’s stay is well over $120,000. Obviously you are not well versed in financial world.