Let's say if I used 1sat/vb and now increasing it to 2sat/vb, I don't find any reason why it shouldn't broadcast it.
This depends on transaction (virtual) size. Note that BIP125 refers to the absolute fee, not the fee rate.
If the fee rate for the original transaction is 1 sat/vbyte and the replacement transaction has the same virtual size and is made with the fee rate of 2 sat/vbyte, it meets the BIP125 requirements and should be accespted by the nodes.