How exactly do you 'put a little pressure on Wikipedia' as an advertiser? It's a hive of independent contributors who, overwhelmingly, draw no money from the Foundation. Very few care at all about advertiser-friendliness.
Any communication to any particular editor suggesting warmer-treatment-for-money risks a big backlash, and provides little assurance of warmer coverage.
On the other hand, even without advertising, big interests can and do try to massage their Wikipedia entries indirectly. If they have a legal case against content, they can and do threaten legal action – again, no advertising link required.
There may be good reasons for excluding advertising. Since an important core of contributors hate the idea advertising, simply keeping them happy may be a good enough reason, and as long as annual donation drives generate plenty of money, why not?
But I don't see where advertising would add new motivations or mechanisms for commercial entities to meddle in article content, especially if proper care were taken to separate and automate ad functions.
In order for an advertiser to have sinister influence, you'd need to assume a bunch of other changes which weaken Wikipedia's resilience. Advertising could be implemented in a way that helps prevent such weakening-changes from happening. And if any org could pull that off, Wikipedia could.
That said, I still understand why, given their community's biases and their success with donation-drives so far, they have not seriously considered ads in many years. Don't mess with what works is usually a good principle.
Also, the organization that handles funds – the Foundation – has very little special editorial power, and their actions are especially transparent. (For example, their real names are necessarily known, whiich is not the case for other editors.) Attempting to influence content by being an advertiser, then making ad spends conditional on favorable bias, would be about the worst possible way to try to influence Wikipedia content. You'd be spending a lot, via a path that's under the most scrutiny. You'd probably prompt staff to be extra harsh on you to avoid any appearance of infuence.
Anyone who really wanted to spend to influence Wikipedia would just hire editors outside the funds/ads-handling organization. That threat is larger, and unaffected by the presence or absence of advertising.
I also worry about the increased tracking on politically sensitive pages or controversial topics.
Wikipedias force in this regard is that their operating budget is small potatoes: they can easily afford to shun any one donor - commercial or personal.