Behold the awkward Portuguese declination system !!
All right, I'm changing my statement into this:
Anyone who says they aren't scared of this is a goddamn mathematician.
I think the table is useful in one way: It tells the learner that adjectives are a problem in German and that the learner should pay attention to them as he/she gets input in German.
You can compress the table into reasonably concise rules, but I think you have to memorize the article/ending pairs anyway if you want to write/speak with any fluency. Following an algorithm, such as "If ein or eine, use Strong declension", takes too much time. The information has to be at your fingertips, like the sequence A B C. Absorbing fixed phrases like "ein guter Freund" until they sound as natural as "A B C" is the way to go.
Given that, I would not recommend memorizing all the cells of your table. Many of the cases are used rarely. Reading a book and paying attention to the endings will let you quickly memorize the endings for the most frequently used cases. That way, you acquire the ability to build your own sentences (and get a huge boost to your motivation) in the most time-effective (and least boring) manner.
I can't stress enough how much rather I'd read a short book in German than study a declension table.
When I read in German, the mentioned rules of declension help me to understand sentences.
Example: Bei dem Test mussten wir das syntaktische Gefüge mehrerer Sätze analysieren.
It is important for me to notice that that 'mehrerer Sätze' is in the Gentiv case. The rules help me to prove that it is so.
I don't use rules for building sentences but for analising them. I agree that the table of declension is useless when you want to speak fluently. But I don't think it is useless while getting input.
They must have about 5 ways just to say "this."