Well at least you can't accuse me of not responding to your question "What is the downside of cutting up your kids' grapes?" 
The downside of fussing to the extent that you apparently do about something that is not considered a risk for school aged children like yours is exactly as I described. It is a considerable downside, as I have shown.
There is the additional one of you losing all credibility in the eyes of your children as a result of your ott behaviour around grapes. That may not be an issue yet, but in a few years your older child will be gaining more independence, getting out among peers more, and your inappropriate focus on things that are not dangerous will result in your child rolling her eyes even more than young teens normally do when you try to give advice. If you are not able to distinguish between real and imagined risk, your child may not take you seriously.
Because there is a huge BENEFIT to them in doing those things. That was exactly my point in posting. Those risks are worthwhile because they absolutely loved having those experiences and it was worth the considerably higher risk.
The idea that because children enjoy an extremely dangerous activity it can be allowed can lead to all sorts of sticky situations. Children's enjoyment of tuktuk rides is not really a factor that should come into adult decision making about whether it is appropriate any more than children's enjoyment of watching X rated films and drinking rum and Coke should come into a decision on whether to let someone off to a 13 year old's birthday party.
There is a huge benefit to international travel.
There is no benefit to allowing children to do dangerous things while traveling internationally. Dangerous things often include drinking local water, eating meats prepared by street vendors, riding in tuktuks.
There is a huge benefit to allowing children to climb and swim.
There is no benefit in allowing children to do these things unsupervised or without lifeguards or contrary to posted warnings, in areas not suitable for climbing or swimming, in weather unsuitable for climbing or swimming, alone, in the dark. There is nothing to be gained but embarrassment of your children if you insist they wear a flotation device when swimming to avoid the danger of drowning.
There is a huge benefit to allowing children to socialise with peers and go to parties.
There is no benefit to allowing children to go to parties where they will drink alcohol, do drugs, have sex, watch X rated films, or associate with children who shoplift or do graffiti, and much , much more.
If reminding a 7 year old child to chew grapes about a hundred times while she is eating them is not the behaviour of a super-anxious person I don't know what is.
Giving your 7 year old a knife to cut the grapes herself would be a better idea than the deluge of reminders. There is a huge benefit to children in learning a skill like that. There is a huge risk to children in you indulging in the level of anxiety you have described while they do something benign that they are well equipped to do, and especially when you yourself have bought the thing that is apparently so dangerous.
Don't buy grapes if you consider them so dangerous that your behaviour as described is warranted.
And wrt the aspersions you are casting on stats from the US on pediatric deaths from choking on grapes - if this was actually a problem of any significance whatsoever, grapes would be banned from schools the way many schools ban peanuts and latex products. Whole grapes are served as part of school lunch menus. School age children are assumed to be able to eat grapes safely.
ucfoodsafety.ucdavis.edu/files/26420.pdf
The U of California extension programme is a public educational programme. Here is its data-driven advice on food safety in the context of lunchbox contents. The advice on cutting grapes applies to 'preschool children'. They are concerned about the 'high risk' of food borne illnesses (esp E.coli) to children under 5.
www.healthychildren.org/English/health-issues/injuries-emergencies/Pages/Choking-Prevention.aspx
The American Academy of Pediatrics suggests a cutoff age of 4 for whole grapes. (See list under the heading 'Keep the following foods away from children younger than 4 years:') Again, this is data-driven advice.
From Nationwide Children's Hospital (Ohio), quoted in National Science Daily:
www.sciencedaily.com/releases/2010/02/100226212559.htm
In order to reduce the risk of choking, parents and caregivers can do their part by following these safety tips:
<span class="italic">Do not give children <span class="underline">younger than 4</span> any round, firm foods unless they have been cut into very small pieces. Cut hot dogs lengthwise and cut grapes into quarters. This changes the dangerous round shape that can block a young child’s throat.</span>
<span class="italic">Do not give <span class="underline">toddlers</span> other high risk foods, such as hard candy, nuts, seeds and raw carrots.</span>
<span class="italic">Never let small children run, play or lie down while eating.</span>
The last suggestion implies that allowing unsafe eating conditions contributes to the danger posed by the shape of the food as well as rendering any other food hazardous. Again, this advice is data-driven.