What are the reasons the Standard can't fly the Lume Cubes? Is it a lack of power, creates unstable flight, mounts not made for it? Inquiring minds want to know. If you aren't old enough to remember that tag line from an old ad, please ignore it!

Who said you can't fly with Lume Cubes?

It's a simple answer, just that thee Standard model sells less, and so Lume Cube only made brackets that fit the shape of the popular Phantom 3 Advanced and Professional models, landing gear.
Yes, as you stated nothing available to hook them up.
No reason you can't use them, but you would need to modify the brackets, or have a pair 3D printed that would fit your legs properly.
They have Typhoon brackets, and recently brought out those suitable for the Autel X Star drone as well...
http://www.lumecube.com/164.html

RedHotPoker