I'd hazard a guess that many factors come before tone when choosing wood. Strength, stability, cost, availability, appearance and weight are a few off the top of my head. The balance of importance between these factors will change depending on other factors, whether budget or high end, painted or natural/stained finish, etc.
Some woods might have gorgeous grain but are too heavy, some woods might be very light but lack strength. Imagine various woods and their attributes in a Venn diagram and the ones in the centre that have the required mix of qualities have become the standard woods for guitar/bass building and have become known as 'tonewoods', but I suspect tone has had little to do with the choosing of these suitable woods over the years.
Now in the day of excess wealth marketing is king and 'tonewood' is an important word in marketing only.
Find any wood that has the required strength and stability and I'd be very surprised if it couldn't be used to make a great sounding bass, it just might be very heavy, expensive or boring to look at.
To take it to its extreme, are they any woods that have the needed strength, stability and weight but are unsuitable purely because of their bad tone?