True, but we also pay -- in whole or in part -- for websites, newspapers, magazines, commercial radio, etc. This doesn't change that fact that publicly supported media such as the BBC are (justifiably) held to a different standard of public accountability because of their special legal position within the media market -- or just outside the media market, as the case may be.
Your premise that the BBC should be "justifiably held to account" more than any other PSB is not well made.
You either have permission to broadcast as a PSB or you don't; the funding stream is largely irrelevant to that legal requirement to provide a standard of service acceptable to Ofcom. Lower standards apply to non-PSBs, but they are still regulated to an extent.
There are legitimate alternatives to accessing media without a TVL, and an increasing number of people use that route, so the tired old argument that
"I have to pay for the BBC, but I don't watch it"
has become somewhat redundant.
If people have a fundamental objection to the BBC, they are not forced to fund it. They can watch programmes free of charge from commercial FTA 'catch-up' services, or pay for Netflix, Amazon Prime etc.
As an analogy: my next door neighbour chooses not to have a car, so pays no Road Tax, as he catches the bus travelling on the same roads. I don't insist on a "better quality of road" for my car, or complain about his choice not to pay Road Tax for his non-existent vehicle. Similarly, he doesn't complain about me paying for something I choose to have.