It's much more complicated than that. The law doesn't wipe the slate clean. Rather, it gives the debtor an affirmative defense against a lawsuit after X years. It does not stop a debt collector from trying to collect on otherwise uncollectible debt (phone calls, letters, calls to friends, family, and employers if the debtor doesn't respond). Additionally, debts barred by the statute of limitations can sometimes still crop up as "zombie debt" years or decades later. Collectors can (and will) put a new records on a person's credit report, preventing most debtors from rebuilding their credit.
When a debtor stops paying debts entirely, it can start a whirlwind of problems. They can be barred from finding housing, certain types of employment, their actual current jobs (certain professional licensing require financial responsibility). Additionally, most debts end up in the hands of collection attorneys (CA) who will sue en masse to obtain judgments. This effectively stops the statute of limitations and gives the CA 10 years, 20 years, or a lifetime to collect the debt. In these cases, a well-timed bankruptcy is (and should be) an option for people. In some cases of debt -- student loans for example -- the debt is presumed non-dischargeable and can create a lifetime of hardship for the debtor.