You have the right idea, but your pragmatic solution does not require to change the grid girl system, so why not keep it?
From your link:
" The grid girl concept is a controversial one and was scrapped altogether by the World Endurance Championship at the start of the 2015 season. At the time, series CEO Gerard Neveu said: 'For me, that is the past. The condition of women is a little bit different now.' "
http://www.espn.com/f1/story/_/id/12948330/sebastian-vettel-monaco-grid-boys-point
Now, you may disagree with him, and many others may disagree with him, but that is one of the whys for many people.
I suspect that the main reason for dropping grid girls is commercial. Women fans currently make up 40% of the audience and the organisers are keen to appeal to the untapped part of the market, including attracting sponsorship and advertising from companies selling to women and companies who don't necessarily want to be seen to be behind the times on gender issues.
Michel Boeri (who instigated the grid boys in your link) and Gerard Neveu both probably have their heads screwed on and their financial priorities to the forefront.
It's worth noting that F1 lost one-third of its global audience between 2008 and 2016. It is reported that young people especially are not getting involved so much. TV viewing figures have reportedly dropped by 40 per cent among the under-25's in the USA since 2000.
They may be gambling that they will, in the long run, win more fans (and thereby money to keep the sport going) than they will lose.
It's true that declining viewing figures is not just a problem for motor sports, especially since the rise of the internet and the economic downturn after 2007, and it's also true that some of the decline is down to motor sport moving (in some countries) from free-to-view to pay channels, but it still means motor sport is trying to up its appeal.
The other hidden factor (as regards the general appeal of the sport), imo, might be that gas-guzzling machines are not seen as universally cool and classy as they used to be, given that in the world outside motor sport, they are increasingly seen as contributing to adverse climate change and choking up the air we breathe, and that issue has been on the rise and likely to continue to become more prominent in the future.
F1 can't afford to risk being a declining brand in the future.