Question about CheckTx behaviour

Hi all,
I am beginning to play with Tendermint and I have a question about CheckTx() function. Reading the doc online (https://docs.tendermint.com/master/spec/abci/abci.html#checktx), it seems to me that this function is used to check if the transactions can be inserted in the blocks or not (i.e. roughly, they can be passed to DeliverTx()). I thought this function was launched only by the node doing the transaction. Instead, all the network nodes run CheckTx(). Is this behaviour normal? I would need that only the node creating the transaction runs CheckTx, not all.

Thanks for your help.