In normal circumstances, where they can raise the amount the next round should have (i.e. one that they can invest with a good return) this isn't helpful. More capital for the fund doesn't necessarily benefit them - they need enough pledged money for the fund, but if they get the ability to pay twice as much for the same startups, that only decreases their take-home carry after the fact; if they have so much capital that they have to invest it in worse startups just to invest it in the expected timeline - that means worse results and less profit for them; if they raise extra capital for the fund that's sitting unused, then it decreases their overall profitability ratios and again means less profit for the VCs personally.
However, if it's difficult for them to get enough investors for the next round (e.g. during an economic downturn) then yes, in such particular cases the PR advantage might be useful. But it's not in most cases, and not now, and the impact isn't that much - the organizations who invest in VC funds (i.e. the limited partners) aren't stupid as well, they can afford to do a lot of due diligence and all the data for the valuations and discussions and doubts about the valuations is available for them. You could just as well argue that if they inflate valuations, then the community of limited partners might think that they're not prudent with their money and avoid investing in their next fund. PR smoke and mirrors works well on the general public, but less well (though not at zero effect) on the large investing institutions.