What would be the consequences if P=NL
$NL=P$ is not considered likely by the experts.
I found a few SE questions on this topic: [1] [2]
The corollaries include:

$P\subseteq L^2$ by Savitch's theorem
$NC=P$ by the Squeeze theorem
$EXP=PSPACE$ by $P\subseteq polyL$

I would like to include or exclude $P=L^k$, $k\in[1,2]$, but I have not collected sufficient evidence for or against that conclusion.