It's this sudden surge of people needing ventilators and ICU beds that overwhelms the healthcare system of an area, causing repercussions on those that are sick for other reasons or get injured in accidents. For instance, in Italy cancer screenings on vulnerable subjects have been postponed for months, if not a year, due to the ongoing pandemic. Who knows how many people have now a higher risk of cancer due to hospitals and clinics being overwhelmed by COVID patients.
COVID vaccines are not sterilizing, but it's getting quite clear that they somewhat reduce the circulation of the virus too by reducing the viral load of symptomatic and asymptomatic carriers. At least they greatly greatly reduce the strain on doctors and avoid disruption of society at large, which is by itself a solid choice for mandating them.
The only possible choices here are to a. neglect the virus, with potentially serious social repercussions and loss of human lives, or b. resort to containment measures, which hamper the economy and are deeply unfair towards vaccinated people which objectively risk much less from the virus, or c. mandate vaccination, which is the only choice that avoids lockdowns and (most) deaths.
Also, vaccine mandates aren't anything new. That's how rubella, diphtheria, polio, smallpox, mumps, .. have become a thing of the past. They've been put in place on for decades, and no-vax movements have always been small and irrelevant before before social media came with droves of dubious content.