Hi,
we do have the same problem and we solved it with a workaround.
You can use the hubspot workflows functionality in order to set the “close date” property to en empty value when creating a deal.
So, if you would like have this functionality set active from e.g. today onwards, you need to define a deal workflow as shown in the pictures below:
workflow - actions
workflow - suppressions
Hope this could suit your needs.
Pleaes also check before setting this workflow active, if non of your old deals are affected.