There's nothing wrong with a rotary euphonium any more than there's anything wrong with a rotary tuba. Get over all that stuff. Golly, aren't French horns rotary instruments? Aren't some of the best high-end trumpets in the world rotary horns? Well, best not to go there.
Re intonation: If your rotary euphonium doesn't play in tune, then there's something wrong with YOUR rotary euphonium. There are virtually countless numbers of rotary euphoniums in use in the German-speaking world, and the Russians have traditionally liked them as well. You think they're all crap and aren't in tune with themselves? Try listening to a few things on Youtube. I have a 1965-ish Amati oval rotary euphonium -- hardly a pardigm of brass instrument qualtiy -- and it's perfectly fine (for an oval euphonium). It doesn't have a range problem and it doesn't have an intonation problem any worse than any non-compensating 4-valve piston euphonium does.
There ARE some differences, and these can matter in terms of blending in sections -- which is why in high-level or professional organizations you rarely see rotary euphs mixed with piston euphs. But in fact the same thing can also be true of rotary and piston tubas, though normally no one makes such claims. The dimensions are a bit different in the rotary vs. piston implementations -- in particular, the length of tubing between the receiver and the valve block -- and this will affect intonation characteristics because the amount and placement of conical tubing will differ. For this reason and others, there will be some tuning DIFFERENCE between a rotary instrument and a piston instrument (as they have normally been designed and made). So it's harder for them to match in their intonation characteristics, and the tonal quality will be a bit different, but that's about it.
A BIG difference, of course, is that most high-quality and preferred euphoniums (in the English-speaking world!!) are COMPENSATING instruments, and there are VERY FEW compensating rotary instruments. But there are both advantages and disadvantages to a compensating instrument.
Why the dearth of compensating rotary instruments? Basically that's all about simplicity of fabrication, weight, and resulting playability. Think about what a compensating rotary valve would look like. There are a FEW of these around, but not many. A compensating instrument will play very differently and have very different intonation characteristics than a non-compensating one. "Different" -- not necessarily "better" in an overall sense. Non-compensating instruments are not "barbaric". An argument can be made that they are the more "pure" form of the instrument and provide better and more uniform tone and sound quality across the range. But this again does speak to the issue of blending.
The other issue (and it may seem silly, but it's not) is that if you're playing a rotary euphonium in a standard American or British musical group, just exactly where do you sit, eh? Think about that for just a few minutes. Talk among yourselves. It ain't pretty. Either some "normal" euph player gets an earful of non-compensated euph, or some poor tuba player does, or maybe some poor trombone player. Bells clash together -- with resultant clanging and harsh language. But wait -- that happens with any classic front valve euphonium or baritone! However, it's still an issue.
A lot of this is cultural (or national origin) inclination. There is no "upright British style" rotary euphonium. In terms of rotary and piston tubas vs. euphoniums playing well together, perhaps this is just because the rotary and piston tuba players are better musicians and can work around those intonation characteristics. I've played both piston and rotary tubas for decades and never had a problem matching pitch with section mates, no matter who was playing which type of instrument. Or maybe euphonium players just have more refined senses of pitch and intonation.
I'd be perfectly happy to play a 4- (or 5- !!) valve rotary euphonium in any venue I'm ever likely to encounter. But if you want to feel like one of the in-group in a US/British band, stick with a top-valve (which means "piston") instrument. All those front-valve American baritons/euphoniums are a thing of the past, right?
And oh ... Leaky water keys? Get new corks for them. I like the Valentino synthetic ones. They're cheap and easy to install. Your water keys shouldn't leak under any circumstances. That in itself will throw off your intonation. Now your standard British-style upright valve instrument WILL generally leak like crazy through the bottom of the valves (it's designed to!), and make a mess of your pants. But there are ways to avoid that (covered in other threads on this forum).
Gary Merrill
Wessex EEb Bass tuba (DW 3XL or 2XL)
Mack Brass Compensating Euph (DE N106, Euph J, J9 euph)
Amati Oval Euph (DE 104, Euph J, J6 euph)
1924 Buescher 3-valve Eb tuba (with std US receiver), Kelly 25
Schiller American Heritage 7B clone bass trombone (DE LB K/K10/112/14 Lexan, Brass Ark MV50R)
1947 Olds "Standard" trombone (Olds #3)