Technically the journalists should have editorial independence and a firewall between them and marketing. So they could in theory investigate their own paper's revenue stream.
Although in this case they wouldn't have to frame it in such stark terms because ad tech is widely used.
“Stuck” may not be the best word for a profitable journalism company that ensures its readers that they aren’t being tracked nor individually manipulated.
Are there any digital news outfits that don’t subject their paying readers to unethical (IMHO) advertising?
Even with the BBC though there are conflicts of interest.
For example, when the BBC introduced compulsory logins for its iPlayer service so that it could, amongst other things, form political profiles on users just in case viewers decided to be in the audience of it's political shows such as Question Time.
I distinctly remember hearing the BBC News team interviewing the BBC's own staff and coming to the consensus with themselves that they were "striking the right balance".
There were no descenting voices on the programme and discussion about why creating political profiles for people might be a bad thing.
Radio 4's 'Feedback' [1] bills itself as "The programme that holds the BBC to account on behalf of the radio audience" and frequently interviews BBC employees.
Obviously there are fraught incentives from them paying for their own criticism. Not sure cancelling the program would improve the situation though.