They likely already charge what the market will bear, to maximizing revenue, such that increasing the price lowers revenue. Raising the price by 5% as a straight pass-through means lowering total revenue. Depending on the elasticity, the consumer price change could be 0 (assuming no one will pay for a higher price), but is almost certainly less than 5%.
Companies will sometimes overtly pass a cost on to the consumer in the hopes of creating political pressure against that cost. For example take a look at your phone or cable bill and how they itemize every tax and fee they have to pay and pass along to you.
If one of those taxes were removed, do you think the overall cable bill would actually go down, and stay down?
Just like VAT increases are not quickly followed by price increases
A myth.
The myth is that a VAT increase (for instance, 7% => 10%, a couple of years ago) would shrink the business' margins : for 100€ paid by the customer, 93€ used to go to the business before the change, and only 90€ would go after the change.
Of course, and this is a massive surprise, all prices increased : the product now costs 110€, with 99€ going to the business and 11€ as VAT
So yeah, I'm pretty sure I know how my taxes work. That said, I can only speak about here in France, as I do not know how it works in other countries.