Use of proof of work in bitcoin
Imagine attacker introduces 100000 rogue nodes in the network and their goal is to send false information about transaction validity ...


That's no possible. Every node validates blocks and transactions for itself. It doesn't matter what another node tries to represent - if the block is invalid, it's ignored by the receiving node.

Proof-of-work is unnecessary for determining block validity.

What proof-of-work does do is makes block generation expensive. Without it, nodes could generate blocks cheaply, rolling back transaction history by publishing replacements for previous blocks willy-nilly.

To rewrite a previous block, a node must not only rewrite the block its self, but all of its descendants. It must re-do all of the work that was previously done.

To re-iterate: nodes validate transactions and blocks for themselves. Proof-of-work doesn't convince nodes of block validity. It convinces them that a certain amount of work must have been performed to produce the block.

A node uses the cumulative proof-of-work when faced with a choice of two or more valid block chains. The one with the most proof-of-work is used to build the global transaction log.