it's not free to make an inscription. they do have to pay
Only if that transaction is broadcasted in P2P way to other nodes. In case of almost 4 MB transaction that started Ordinals, it was mined by Luxor. One pool with sufficient hashrate is enough to make the chain bigger. Attackers could reach 1% of the hashrate, and then they can put a lot of inscriptions for free every 100 blocks.
1% of total hashrate to acquire would cost close to 150 million $ ( i did some calculations in the past and at that time the infrastructure had a cost of 16 billion ) , not to mention the power cost which is a nice amount . So , these transactions will not be free for them , even if they push them with zero fee .