It's not immune to ALL damage except slashing
There are a couple of RAW ways to destroy a net:
- Dealing 5 points of slashing damage.
- A caster using a fire based spell which states it ignites flammable objects.A net has no protection against fire and would thus be destroyed.
- A disintegrate spell targetting the net since disintegrate turns objects it strikes into dust.
- A wish spell.
- And many other magical solution for which the spell would appropriately remove the net.
But as for using bludgeoning or piercing weapons, the answer is no. The net text specifically states that slashing is the required damage type. And yes, if a creature lacks slashing damage or some other logical way of removing the net such as breathing fire on it, then it would need to rip itself free with the strength check.
The DMG pp. 249-250 has the statistics on object health and AC values, indicating that the net is made of either cloth, paper or rope, and is designated as fragile. If it were made of metal, the AC would be around 19 as that's where iron/steel starts out.