Don't trust online reviews word per word. To the reviewer it may sound one way, to you another. You are happy the way it sounds
Introducing a DAC may help "resolve" some stuff (pun intended) or it may just be different sound.
British/American/Euro/Chinese blah blah was 70s parlance.
These days, if amps/speakers are designed well they will sound good. If not, they sound ... well, you know...
If a manufacturer told me that this system is built for rock or classical or jazz or hindustani, I'd be very suspect.
The design is lacking something. How does electronics know music genre
British sound is "treble rolled off" and a "voice bump" thus sounding warm.
American sound is well "may be not the above".
Possibly the Brits in the 60s and 70s thumbed their nose at America.
Does not mean American amps/speakers are bright in the absolute sense. No.
All amps/speakers just are what they are.
You as a listener decide if it is to your liking (warm/bright/rocking/fuzzy/engaging/dull/..../....)
As FM @SwaroopKS suggests, get a CCA and throw it in just for kicks.
If not anything, it will give you a streamer/DAC combo. Different sound.
I can vouch for the little sucker. It punches way above it's price point and brings convenience.
Also suggest you hookup with local FMs and borrow or audition a DAC in your rig.
This will clear up whether you are really missing details and should attack your bank (or someone else's
Since you claim you are the cautious type means you have the patience to try stuff out before splurging.
Enjoy the hunt.
Cheers,
Raghu
