Being able to scale individual components/services will be the most efficient solution, but if there doesn't happen to be a particular bottleneck that bogs down everything else (besides the database), it seems like the traditional monolithic load balancing approach may not be so bad.
Especially compared to the effort of trying to split an existing monolith into microservices. And if there are other bottlenecks, you can focus your effort on improving or isolating those parts.
(I only have intermediate experience in this area and certainly way less than you do; definitely not trying to claim anything authoritative.)