Matching fully balanced with unbalanced.

I prefer the single outs/ins on my system. Long cable runs are not an issue for me, and really the primary reason to run the “balanced” outs/ins is mostly this. Also, as mentioned, few systems are truly “balanced” anyway...

Not sure the science of your question was not answered already...? 
If *balanced* is 'pseudo balanced' i.e. achieved by opamp implementation as compared to 'fully balanced' implemented by two seperate strands of amplification within one source unit, the notion is that fully balanced is superior technically to a 'quick fix' opamp implementation. 
So, if the equipment is not a fully balanced design (looking at the design diagram was already mentiond) THAN it will by deduction appear to keep the opamp out of the source line AND USE THE SE (single ended) connection. 
Drilling further into the science of whether the addition of on opamp is beneficial to sound quality can be answered by listening, what has been mentioned. 
BTW, that opamp chops a full audio sign-wave into a negative and a positive, so it's up to the beholder to decide whether this is of no import to the signal further passed down the line. 
Again, if the final stage the poweramp has a pseudo balanced input option, the use of this also involves an opamp to first combine the two halve waves, ahead of the actual poweramplification stage(s). 
Common sense, at least, suggests that this again will not lead to any signal improvement but rather to a degree of its deterioration. 

Not sure this fully will answer the question regards any scientific proof etc.. 
To do THAT, a signal analyser would need to be called for plus engineering experience in explaining the results generated. 
M. 

surfmuz OP7 posts05-23-2020 3:45pmOf course testing and listening that for sure, but could any body throw scientific base under this topic?

Sure simple, what comes out of 99.9% of hiend poweramps is SE (single-ended), the speaker terminals are + positive and negative is at ground potential.

Cheers George.

BTW, that opamp chops a full audio sign-wave into a negative and a positive,

Huh?? No it doesn't. An opamp has two inputs, inverted and non-inverted, and otherwise is a DC coupled amp with very high gain. for audio purposes, to control the gain and allow the opamp to operate in a linear fashion (otherwise the output tends to spend a lot of time at one rail or the other), feedback is applied. The resulting gain is thus then the ratio between the input resistor in series with the inverting input and the value of the feedback resistor. It does not chop the signal or anything like that- the output is single-ended, and in phase with the '+' input and out of phase with the '-' input.

Tnx, atmasphere...full and argumentative explanation. 
 I knew the topic isn’t easy... but consensus should be reachable:) ... However, Physics is not Psychic. :)