Hi!
Thanks for the video.
No connection is broken as your video proofs.
Maya transform nodes can only have one input, either a key, an expression a constraint or any other connection to an other node, you can check this in Node Editor.
When you add a keys constrained object to an attribute that has no input, there is no change for the current connections, but if you add keys to an attribute that is already connected / constrained, then the connections need to change, there is no other way.
If you add keys to an attribute that is constrained the connections are not simply replaced, you get a blend node which allows you to keep the previous influence from the constraint and add the influence from the keys, but you can define the ratio on your own.
This value will be different for everyone, so whatever value is chosen here will not fit everyone's need in every case.
You maybe want to keep 100% override from the constraint, but others maybe want to completely override the constraint (as done currently with "0") or maybe prefer a default value of "0.5" .
So my previous recommendations are still all valid.
a) Only add keys to attributes that are not controlled by the constraint.
(This does not change anything related to the constraint and does not require the blend node)
b) Use the Blend Parent attribute to control the influence of the constraint and keys.
(Maybe create your own script for setting keys that sets the blend value as you like at the beginning.)
c) Use Animation Layers to add additional keys.
...
There are for sure more options.
You can also add a suggestion to Maya Ideas to be able to set a custom value for this in Preferences:
Help -> Speak Back -> Maya Ideas
Again, nothing is broken or disconnected when adding keys to a constrained object, you just would prefer an other default value for blending.