Mario would be a really bad character without these tools or other tools of equal value to replace them
This is subjective/opinion. The assumption of this statement is necessary for your conclusion to be true, but the problem is assuming the premise to be true. A lot of characters that you would consider better than Mario don't have a lot of the same tools as Mario and yet they are not really bad characters. A better statement that I think can more easily be agreed upon as sound is this:
Mario would be a much worse character without these tools or other tools of equal value to replace them
Luigi is a Mario clone
Luigi doesn't have these tools or other tools of equal value to replace them
Therefore Luigi is a much worse character
All this does is make Luigi be below Mario on the tier list. Is last below Mario? Yes, but so is just one spot below. To include characters in between Mario and Luigi on the tier list these characters must be included in your logic argument and must have a clear relationship defined that objectively outlines what they have and what makes them better. Going by your initial logic statement, there is a jump you're making by saying the lack of tools makes him bad and you give nothing to prove that lacking those tools makes him bad other than the assumption that the statement is true. What you have provided is proof that lacking those tools makes him worse than Mario, but again, worse than Mario doesn't mean worst character on the roster, more proof is needed to show Luigi is inherently bad.
His slowness is definitely an objective measure that helps the case of him being the worst, and in my opinion doesn't define him to be. Considering there is more to the game than simply speed, he has better recovery and edge guarding options than characters ranked above him, and even a better projectile than some (as outlined by maafia) but those tend to be ignored because of the stigmas against Luigi.
I really think if tier lists are going to be made then there needs to be more objective measures used than opinions and how people feel doing individual eye tests against each character. Here are metrics I feel have more substance in ranking characters, and the weight of these metrics can be discussed separately: average tournament placement, character matchup score (calculated by quantifying matchup favorability and averaging all matchups), complexity score, difficult to operation score.