Okay, I am Taking the Pro Audio Plunge

I believe the Neumanns would an excellent upgrade. Though since you listen at midfield distances I believe this would be a better fit https://www.neumann.com/en-us/products/monitors/kh-420?variant=505988

If I was in the market for new monitors I would definitely be interested in these.

Don't under estimate what a tri-amped speaker can do and depending on what kind access they give you to the DSP engines, the results could be pretty spectacular.

Depending on what type of music you listen to and how loud you listen to it you may need to add a subwoofer system to them, but if you are replacing a non-subbed 2-way speaker with the Neumanns, they should blow your current system clean out of the water.

A couple of things to be aware of. These speakers are balanced input only so if your preamp is single ended, you would need an adaptor and you would loose some of the potential performance.

If they grant you full access to the DSP the learning curve is...well never ending. Mainly because the ability of the ear to improve and understand what it is hearing is slower than the capabilities of what a speaker of this nature can do.

Also pro audio manufactures don't normally offer a trail period, so if one is a requirement, I would get written confirmation from them that a trial period is an option. 

Depending on what type of music you listen to and how loud you listen to it you may need to add a subwoofer system to them, but if you are replacing a non-subbed 2-way speaker with the Neumanns, they should blow your current system clean out of the water.

I have DSP and Parametric EQ capability already through my WiiM Ultra. My Fiio K13 DAC also has EQ functions (though I haven’t messed with them).

Forgive me for having doubts that the Neumanns would blow my current system “out of the water.” I am sure the Neumanns are great, but my Satori Helios Textremes and BMR HT Towers are no slouches by any measure. Upon further research, I discovered that both pair produce lower THD in the midrange at high SPLs vs the Neumann 310s, Kii 3s, and D&D 8Cs. And the Helios have absolutely absurd bass dynamics for their size. They are one of two speakers I’ve owned that truly have zero need for subwoofer augmentation (though I use an REL Carbon Special anyway).

Further, when one considers the cost of the drivers in the Helios and BMR Towers (DIY and factory-direct respectively), the Neumann’s and similar ilk begin to lose appeal. I have a hard time believing Neumann are equipping their monitors with drivers that would justify >$300 each if sold separately. In other words, I’m unaware of any largish companies with marketing departments and dealer networks that are equipping their <$10K speakers with $300 drivers. And through my DIY experience, I’ve learned that price does generally correlate with performance when it comes to drivers. The caveats to that are some compression-driver tweeters and the Tectonic BMRs. 

Anyhow, last night I made some small position and EQ adjustments to the Helios’ and the resulting performance left me wanting for nothing. The performance was nearly as good as I recall from systems anchored by $50K Rockports and $100K of components, arguably better in some regards (at least better than the Atria 2s in terms of bass). I get that the Neumanns have the theoretical advantage of a dedicated midrange. However, my past experience is that a top-tier two-way speaker will often outperform a 3-way. It really depends on the individual driver quality and implementation. I’ve encountered quite a number of mediocre 3-way speakers under ≈$8K that were lacking in midrange resolution compared to mid-woofers in the $200/each range. 

No doubt the KH420s are a top quality monitor, but I think I’ve concluded I’m content with my current setups(s). It’s not as though my current speakers lack monitor-like linearity or distortion levels. 

@OP Bear in mind that commercial manufacturers are not paying retail prices for their drivers.

But to answer your original question, the areas where studio monitors tend to have shortcomings / disadvantages for domestic listening are:

Predominantly designed for nearfield listening at a distance of 1-2m

Less attention paid to cabinet construction.

Active with the amplifier in the box - a bad location for an amplifier.

Among the studio monitors which can make a case for being used domestically, passive PMCs are the best I've heard. Among the actives PSI are also good.

@OP Bear in mind that commercial manufacturers are not paying retail prices for their drivers.

I do take that into account, however, it’s not as though they get a 50% break on the driver MSRP when they place a bulk order. It’s more like 10-20%. Regardless, most big commercial brands are equipping their $10K/pair speakers with drivers that won’t outperform a $130 Seas or Scanspeak unit. ATC is one notable exception.