In theory, yes. In practice typical insurance requirements are already far below realistic modern-day damages possible from vehicular collisions, and people still routinely drive without even that minimal insurance.

Without better mechanisms to actually meaningfully enforce insurance requirements, changes to those requirements are unlikely to be effective.

The elephant in the room in the US is that although driving is a (very dangerous and extremely socially-costly) privilege, any attempts to hold drivers accountable and take away that privilege from repeat offenders is treated as a rights violation, so instead we just accept many deaths of innocent people from repeat DUI and speeders.