Robots.txt does not stop indexing, and blocking often makes it worse.

Two different instructions

robots.txt controls crawling. It says: do not fetch this. A noindex directive controls indexing. It says: you may fetch this, but do not list it in results. People use the first when they mean the second, constantly.

Google can index a URL it has never fetched. If enough other pages link to it with consistent anchor text, Google can conclude the URL exists and is about something, and list it on that basis alone. That is why the Search Console status "indexed, though blocked by robots.txt" exists, and it catches people out every time.

The trap

Here is the part that gets missed. Someone sees the page in Google, decides to be thorough, and adds a noindex tag to it as well while leaving the robots.txt block in place.

That cannot work, and the reason is almost funny once you see it. The noindex lives in the page. To obey it, Google has to read the page. You have just told Google not to read the page. The block prevents the crawler from ever discovering the instruction that would have removed it, so the URL stays listed indefinitely.

So when is robots.txt the right tool?

When crawling itself is the cost. Infinite filter combinations, calendar pages stretching to the year 3000, internal search results, and faceted URLs that multiply without limit. You block those because you do not want the crawler spending its time there, not because you are worried about them ranking.

Use noindex when the page must not appear in results: thank-you pages, thin archives, staging content, anything with a genuine reason to stay out of search. Use robots.txt when the page must not be fetched. Occasionally you want both, in that order, with a gap in between.

The wider point

Most Search Console statuses are misread in the same direction: as errors to be driven to zero rather than as the system reporting what it did. "Indexed, though blocked" is Google telling you your two instructions disagree with each other. Some statuses genuinely need action, like crawled, currently not indexed, and some are the system working exactly as designed, like alternate page with proper canonical tag. Knowing which is which is most of the job.