The real problem is if we did as you suggest then users would run their node only for transactions
and as soon as it is broadcasted and within a block, they would just shut down that node.

The real discussion by the OP is about having 24/7 full nodes that help distribute the security and
risk through global decentralization which is encouraged by directly incentivizing the transaction node
users. Miners are doing their jobs 24/7 and not intermittently. Nodes should be doing their jobs 24/7
as well, like guards on distant mountains keeping watch of their territory.

Average joe users do not need to nor should run full nodes, it is beyond their capabilities, but
full nodes should be incentivized in some way to encourage new capable people into the full
node field, so we can get the Bitcoin node network from 5,000 to around 50,000+.

An increase in legitimate 24/7 full nodes distributed worldwide is the goal.