Yes, travel insurance is worth carrying for a Pamplona trip, and how much it matters shifts sharply depending on your dates. Outside the second week of July, Pamplona is a calm regional city with unremarkable travel risk; during the Festival of San Fermin, when crowds pack the old town for the daily encierro, or bull run, through the streets, the risk profile changes considerably, and that is the honest reason to look closely at coverage for this particular week.
Pamplona has solid hospital care by Spanish and EU standards, so the underlying medical system is not the concern. What matters more is checking whether your existing health cover extends abroad and specifically to Spain, since coverage rules differ by country of residence, and a standalone travel policy remains the simpler option regardless of what a home plan might technically include.
The encierro itself carries real, well-documented injury risk - runners are hurt, sometimes seriously, in most years, from falls, gorings, and crush injuries along narrow stretches such as Estafeta street, part of the route into the bullring, and the surrounding festival crowds bring their own risk of minor injury or theft in the packed old town. If running or watching from close range is part of your plan, confirm your policy does not exclude participation in the bull run specifically, since some policies treat it as a hazardous activity requiring its own cover, distinct from ordinary spectating.
Keep any clinic paperwork and police reports if you need to file a claim during the festival, since documentation from Spanish authorities and hospitals is generally straightforward to obtain afterward. Many policies also require notice before non-emergency treatment is booked, so check the claims process in your policy wording well before San Fermin week rather than during it, when clinics and pharmacies are at their busiest.