Can one have too many tube components in a system?

No. My tube system is dead quiet. I would know if it wasn’t since they power horns. 

25 tubes, 93db speakers, unshielded interconnects and quiet.

I’m all SS. So YES, 1 is too many tubes.

My father was more than happy to go SS in 1964. Just too many compromises with tubes. Hasn’t changed. Tube rolling, any one?

I'd been 100% solid state up until a year or so ago. 1st it was my eBay score STAX SRM-007tA driving my Koss/Drop 95/X Electrostatic Headphones. This led to my  trading in ALL my PS Audio Stellar Amplifiers for a BAT VK50-SE (with enough to spare to but 8x 6H30's cause the one's inside were "tired"). Then finally, I bought a brand new Jolida 3502p and installed 4x KT150's (sold the unused 6550 tubes that it came with).

I would run that Amplifier for a glorious 8 months before selling it to a good home. I'd demo'd an Orchard Audio Ultra Amplifier and this reminded of the beauty of Class D GaN when done correctly. Driven directly from my PS Audio DSSr. DAC, it was pretty damn good with the "Tubiness" of the Jolida Amplifier. Driven with the BAT Preamp inserted into the audio literally "kicked things up a notch". 

Then I inserted the Joilda back into the fold with and without the Preamp. It felt 2nd order harmonic overload. Not that there's anything wrong with that. But it wasn't for me. 

So I'm now a Tube Boob on the input side of things but Transistors/GaN's on the back end of the chain.

Only if you have to strip down to your undershorts and turn on a fan to stay in the same room with them during the winter...