I have never had any issue with any of my Weber carb cars self priming, mind you they were all using electric fuel pumps.
I guess if it depended on a mechanical pump it might take some priming to fill the float bowls, but I wouldn't feel too good about having one of those rubber squeeze bulbs anywhere near my car. I have seen too many aged ones where the rubber starts cracking and eventually leaks. Having that happens on a car with electric pump would be very bad with gas spraying all over. Not so bad on an engine that was sucking through the bulb via a mechanical pump on the engine - you'd probably get gas dribbling, but not spraying around.
Not the same issue on boats - if you are using the bulb every time you use the boat you are monitoring bulb condition. On a car where many people don't open the bonnet unless something goes wrong (like the engine seizes for lack of oil, in some cases), the monitoring isn't likely to be anywhere near as frequent.
On the whole, I would think that installing a small flow through electric pump would be a better option for priming. I did that on my old Jensen with a big block Chrysler and sixpack. That was a lot of float bowls and once they dried out after sitting for a week or three, a lot of cranking to get the thing going and the little low pressure pump did the trick (you can plumb it in so it is a side circuit and doesn't interfere with the volume the mechanical pump wants to suck when running).