I somewhat get what you're trying to say (I'm still not sure if you disagree/agree with the OP or are simply trying to reword/reframe his idea to make it better understood), and the analogy has some relevance, but the logic underlying it is flawed, as your argument is parameter intra-dependent (i.e. it depends on parameters that must co-vary properly the argument to hold.), which weakens it substantially. This leads not so much to generalization as it does to the converse, freedom of the parameters, which is bad. The next part was written before this, so I apologize for the lack on continuity. Basically, I just want to clean this up, expand on it, fix whatever is broken, and finally clear it up hopefully.
I don't see the validity of this argument as it's arbitrary, depending entirely on the undefined rate of transfer through this "pipe, tube, etc." of yours, which if sufficient would in fact drain the respective Ocean, as by your definition it is not infinite.. Thus, "nearly infinite" and "infinite" are two totally different concepts, whereas "unlimited" and "infinite" can be used interchangeably if in the right context, such as this thread. The people in this thread are not mathematicians (I exempt myself).
As you've written it, you can also have a puddle with a straw connected to it that drains out the water so slowly that there is always water remaining until it reaches its finite limit. This length of time can be set with the proper parameters to match the ocean and the pipe, giving the appearance of unlimited water in each case, albeit with different transfer rates. The different rates make this arbitrary from a mathematics and logic-based perspective. Now, I showed the two extremes (high supply, high rate = low supply, low rate), and given that they are an effective argument, that means that what I stated for the in betweens holds true in principle.
Finally, to keep things simple, I never incorporated the third main component (1. depletion, 2. source size and 3. regeneration) Namely, you could have an ocean (i.e. large source size) that drains faster than it's refilled (This is one of the most common questions in 1st/2nd semester Calculus, and described by simple differential equations), which leads to the exhaustion of chakra. Whereas if the refill rate matches the drainage rate, the actual amount (i.e. 2. source size) of chakra that one has becomes irrelevant to a large extent because it never changes. It is only relevant in limitations for performing chakra intensive jutsu such as summoning jutsu, Chibaku Tensei, Bansho Tenin of meteors, ..., etc. Note that I ignore the case of the regeneration rate > depletion rate, as while it mathematically possible and would lead to an overflow of chakra/water, it's not relevant here.
Thus, there are infinite ways to get unlimited chakra without the chakra amount itself being infinite using our terms depletion, source size, and regeneration. This is simple mathematics (note: I consider simple to be early college late high school, depends on if you took college courses early, lol) and can be explained using simple ordinary differential equations.
Now, perhaps the manga necessitates our parameters for us, such that ET must have a large chakra pool (e.g. ocean) and a high draining rate, but that is slower than the rate at which his chakra is replenished (see your ocean/pipe analogy above). This situation leaves Madara with unlimited finite chakra, but not infinite chakra in discrete time. However, for basic use of the English language, and not being mathematically rigorous, this is for all intensive purpose infinite chakra, allowing the terms to be used interchangeably despite the fact that they are indeed distinct technically.
It was a nice analogy attempt, but inherently flawed in its design given the lack of constraints/freedom of parameters (co-varying) on which it was dependent (which is OK on these forums). Further it conjures up the proper concept. There are an infinite number of which that lead to the appearance of infinite water/chakra, which leads to the freedom of parameters problem. Another thing is, infinity is not a number itself, just a heads up to people out there that don't know this. It's a concept. If this was a math class or computational science one, I would care about the distinction between unlimited and infinite chakra. However, that's not what this thread is about; thus, I feel that posters have a good enough understanding, and in this context can equate the two terms ("infinite" and "unlimited") based on chakra availability when a jutsu must be cast.