That's exactly right. And, that's how it was until COSPAS-SARSAT came into being, which was well after 121.5 MHz ELTs were required. Satellite alerting is relatively recent in the grand scheme of things. So, while it is a big step backwards, but the system did function back then, albeit not as effectively.

However, the value of ELTs in general is a very open question that's not easily answered. Back in 2000 when the NTSB first recommended it and AOPA came unglued, the cost to convert was up near $5000. Their argument regarding the issue of the cost-benefit ratio carried a good deal of weight in the FAA's eventual decision not to require them. That was also well before a date was set to eliminate 121.5 MHz satellite alerting.

If folks will read the article and the linked reports, they will have a better understanding of the issues.