SpaceX also intends to deorbit two of the functioning satellites in order to test the process.
It's still early days for Starlink, but it suggests that you won't see a host of dead satellites clogging up Earth's orbit. The concern is more one of scale. Eventually, SpaceX hopes to put a constellation of nearly 12,000 internet satellites into orbit. There's no guarantee that SpaceX will enjoy similar or better success rates for all of them. A comparable failure rate would still affect hundreds of satellites over time, increasing the risk of persistent space debris.
Thankfully, the satellites won't last forever. SpaceX already expects the satellites to last five years before they plunge into the atmosphere. It's just a question of how many of those machines make a controlled plunge rather than failing in unpredictable ways.