I'm not entirely sure I follow you. It would be helpful if you explained what kind of contradiction or issue you were trying to gather evidence for. My impression is that you see this table or maybe the concept that such present/future word relationships exist in English as inherently flawed.
It's hard for me to imagine the word will that means "going to" as a present tense verb. Putting that aside, the table you propose works in some contexts.
"If you show up, I will perform on stage." -> "If you had showed up, I would have performed on stage."
"I shall be there." -> "I should have been there."
There are also a whole lot of sentences for will/would, etc. for which this kind past/future translation doesn't work, and that's because English is a language where words and word phrases have multiple meanings. The table (I've never seen such a table, but...) works with some form of those words.
This is somewhat equivalent to pointing out "Light is supposed to be the opposite of heavy, but light is a noun, not an adjective!"
If you're suggesting that teaching such a table has no value: That's not a wrong opinion, but it's not the purpose of this site.