I thought that the ISBN was needed to publish all books[.]
To be clear, NO electronic book "requires" an ISBN. ISBNs are the basically the domain of printed books.
For electronic books, it is essentially superfluous. Much of the things that an ISBN is used for in the "real" world (e.g. sales tracking, returns, etc.) are either not applicable or are accounted for in other ways (e.g. downloads, customer order history, etc.).
Any "need" for electronic books to have an ISBN is dictated by e-book retailer policy and the desire of R.R. Bowker (who distribute ISBNs in the U.S) to make money -- not because it is practical in any way to that medium.
Here is a list of services you might (or might not) need an ISBN for when publishing an e-book through them.
ISBNs are purchased in the U.S. via R.R. Bowker and their MyIdentifiers.com service.
It's a bit expensive, but one thing to consider is that if you use an e-book retailer ISBN, they will be the official listed publisher for that work, not you. This is because whoever bought the ISBN is listed as the publisher and this is non-transferable.
Per this ISBN.org FAQ:
"ISBNs cannot be transferred on an individual basis. If a self-publisher wants to be identified as the publisher, the self-publisher must get their own ISBN. A printing company or publisher services company cannot sell, give away or transfer one of their ISBNs to a customer."
If that makes a difference, you should buy your own ISBN(s).
I also want to publish on other platforms potentially, so should I get one anyway?
The general recommendation is that every edition through every medium (hardcover, softcover, Amazon, Apple, etc.) should have a unique ISBN, so you will likely want to buy a block of ISBNs in this case.
Also note that ISBNs cannot be reused. So if a book goes "out of print" (stops being produced), the ISBN for that book can't be assigned to any other book. So you will likely need more than you think. =)
Are there disadvantages to publishing on KDP without an ISBN if you intend to potentially publish on other platforms at a later date?
Assuming I am reading this correctly, there should be no obstacle assuming that there truly is no ISBN attached to the book (i.e. not even one assigned by KDP). Otherwise, if an ISBN is assigned, not being listed as the publisher for the book could (potentially) create issues.
KDP guide says that they will provide their own Amazon Publishing number.
According to this KDP FAQ Topic, as you note, an ASIN (Amazon Number) can be used by Amazon, avoiding the need for an ISBN on KDP.
Despite the silliness of ISBNs for electronic books, if you can afford it, I would buy at least 10 ISBNs, preferably 100, at least if you are semi-serious about writing (this isn't a one-off thing) and plan to publish on multiple platforms, in multiple formats or multiple editions. ISBNs do not expire and there are no renewal fees. It is best (again, if you are serious) to treat it as a "real" business and make a financial investment in that business.
Note, however, I would shy aware from Bowker's "extended" services, such as bar codes, etc. There are options for that later if need be.
I would also highly recommend you consider offering the book for download yourself. You certainly don't need an ISBN in that case. However, the trade-off are (of course) potentially marketing boost and technical details.