To install and run an LN node, you would also need to install bitcoind, unless you're using something like Neutrino. But if you are already maintaining a 24/7 full node, then you can install and run a Lightning node with it and charge for routing fees.
I get the point, but IMO it sounds like incentive to keep existing node running rather than incentive to run full nodes.
Additionally, unless your LN node have routing path/directly connected to lots of other LN nodes, i doubt you'd get sufficient income/reward.
It was more like a shower thought idea, than a definite solution to incentivize existing/running nodes. Maintaining a full node 24/7/365 has costs, especially on bandwidth. At least there's an idea of incentivizing them, than none, if the Lightning Network scales.
adding soap to your shower thought, to clean up things
imagine an average payment was for a coffee($3) and the routing fee was 1millisat per channel
(yea most users route hopping would end up paying 10 millisats to hop through 10 channels(degree of separation math))
(but where each channel on the route only charges 1millisat)
well for your channel to hop enough payments to make 20cents (0.00004btc) is the difference of
0.00000000001
vs
0.00004000000
so although your gonna try getting the counterpart to pay the onchain CLOSE channel fee. the channel will need to consist of
4000000*$3 to make 4000000 payment to make 20cents just to pay for YOUR initial 20cent channel OPEN cost
$12m channel value your counterpart needs to pass to you for you to claim 1 millisat per payment just to get a break even for just opening a channel at todays onchain fee 20cents.
... think about that