A page is rented space, not yours
A Facebook page runs by Facebook's rules. If the page is restricted or removed, or the account has a problem, your only channel to customers closes.
A website and domain are your own. What goes on it and how is your decision.
People searching Google do not find pages
When someone searches Google for “buy honey” or “dental clinic near me”, the results are mostly websites and Google Maps listings. With only a page, those customers are hard to reach.
Yet they are the best customers, because they are already looking for the thing.
Old posts get buried; a website stays organised
Finding a product post from a month ago on a page is hard. On a website, every product or service sits in its category with the price shown. Customers answer “how much?” and “where are you?” for themselves.
Trust
When payment is in advance or the purchase is large, customers want to check you out. A website in your own name, with an address and contact details, makes the business look more dependable.
So should you drop the page?
No. A page is excellent for reaching new people and staying in touch. The best results come from running both: the page and ads bring people in, and the website gives them the full picture and takes the order.
And an honest note: if the business is brand new and you are still testing whether the product sells, starting with just a page is fine. Think about a website once sales become regular.