Being open source means anyone can independently review the code. If it was closed source, nobody could verify the security. I think it's essential for a program of this nature to be open source.
Discussion
There are levels of open source. There is a level for full read, another for modifying locally, another for opening branches, another for running it in different code local and another for people actually choosing to use different branches, nips, versions, etc
"Source-available" is bare minimum of what Satoshi was talking about
"Open source" is better because it means open licensing in addition to publishing the code