Yeah.
Just like any crowdfunding site.
One possible workaround I thought of would be to provide one BTC adress and give instructions to people who want to fund it and dont own any BTC wallet, to go to a site who sells bitcoins buy some for the desired amount of fiat and pay them out to the given BTC adress.
But usually if something like this has more than 2 steps to accomplish, most of the people will simply not bother to do so. Usually a simple registration form is too much.
As far as I'm aware, the complete service you are wanting doesn't currently exist. Unless the person knows what they are doing, gifting BTC to someone else can be a bit of a hassle. Perhaps this is a business opportunity for you to explore?
I suspect most people would just use Paypal to collect the initial "donation" from friends and family as it is widely known, most people trust it and it is relatively easy to use. Then they can simply move the Paypal funds to BTCs themselves using whatever BTC purchasing service they like (localbitcoins, exchanges etc).
The advantage I see doing it this way, is that it is easier and, as you say, more likely for someone to gift money if the difficulty is lower... and because the money starts in fiat, you are able to actually purchase "Real World™" things before converting the rest to BTC.
Granted, it does require a little bit of manual work on your end (converting Paypal funds to BTC), but hey... you end up with "free" BTC right?? So, once a week/month having to go and source BTC is not THAT big of an issue right??