I think you're completely missing the point on the applicability of a T200 chip for tournament poker.
If you are running a 5/10 blind tournament (typically called a T5-base event), the optimum denominations, breakdown, and blind structure have nothing in common with a T25-base tournament, which has an entirely different set of requirements and thus parameters. There are several good reasons for the T500-to-T1000 2x denomination jump in a T25-base or T100-base set, and those reasons do not exist for a T5-base set/event.
You can't just take a T25-base set or structure and "divide by 5" and expect it to play the same way..... because it won't.
I understand that the 200 makes little sense at first
it allows me to take any 25/50 blind structure and follow it, but just have it divided by 5 instead.
It take 4x 25 to make 100, and 5x 100 to make 500 and 2x 500 to make 1000.
If I divide everything by 5, it will take 4x 5 to make 20, and 5x 20 to make 100, and 2x 100 to make 200.
So the 200 in this case shouldn't be any more useless than a 1000 chip for 25/50 tournaments.
This is flawed thinking, for a couple of reasons.
In a T25-base set, the T1000 chip is a primary workhorse chip for the latter half of the tournament, replacing the T100 which is the initial workhorse chip. Both chips are numerically 1-based, and are thus the easiest and quickest for humans familiar with the base 10 decimal system to count without errors (one hundred, two hundred, one thousand, two thousand, etc.). The T1000 chip also transitions a T25-base set to continue upwards (using efficient 4x and 5x jumps) using denominations that are also the easiest to count and use (5000, 25000, 100000).
Simply dividing by 5 creates a T200 chip that fails at all of those things. In a T5-base set, the workhorse duties are equally shared by the T5 and T25 (and to a lesser degree, the T100) and generally, no chips larger than T500 will ever be needed (nor very many). A T200 chip is awkward and not intuitive (try counting: one two-hundred, two two-hundreds, three two-hundreds, etc.), is inefficient as a 2x jump from T100, and does not serve as a transition chip to larger denomination chips (which aren't needed).
The 200 is .... really no stranger than having the 1000 chip for a 25/50 tournament, which is a "weird" chip to have anyway.
Untrue, for the reasons stated above. It's actually the T500 chip in a T25-base set that has lesser value, and as such, fewer are needed when dealing with a set that contains a 2x transition from T500-T1000.
But this is not true for a 2x T100-T200 transition in a T5-base setting, since the T100 is a partial workhorse chip and the T200 is not. It may look similar on paper, but it is very different in reality.
I will use 5/10 for tournaments. So the exact same as 25/50 but divided by 5. That means, when you're saying I want plenty of 1000, that means I need plenty of 200.
The reason I want to use 5/10 is that it's just easier to combine cash + tour into one set that way without needing plenty of chips. Plus I will have 20 instead of 25.
As shown above, it's NOT the same, and you won't need 'plenty' of T200s, since it's not a workhorse chip in a T5-base set/structure.
Good T5-base and T25-base tournament structures are created to best utilize the chip denominations available in each set. One is simply not 5x (or /5) of the other.
And I don't advise using a T20 chip in a T5-base tourney set, either -- T25s are a much better choice for workhorse chips, for similar ease-of-counting and efficiency reasons. Regardless, using a T5-base structure with a chip set that contains T20 chips (vs T25s) will require modification.
Regarding cash sets, generally speaking a $20 chip works better for low stakes (using 25c, $1, $5 chips), and a $25 chip works better for higher stakes (using $1, $5, $25, and $100 chips).
But using the same set for both cash and tournament play is simply asking for trouble. Too easy to compromise the set, and more difficult to ensure the integrity of the game. A single error can end up costing more than the price of additional chips needed to create separate sets.