As someone who doesnt know enough about the subject to have a valid opinion, it sounds to me like a gunsword, which has floated around in peoples mind since the gun was invented. There are even real life historical examples of them floating around. That's on one planet over lets say a roughly 500 year period of firearm use. 

It seems silly to assume that 100 quadrillion people over the course of... okay I have no clue how long star wars' timeline is. It seems silly to assume no one has ever tried to build one before. I also don't see what would stop a non-force sensitive from building one themselves, unless the technology is a closely guarded secret of the jedi.

 I'm in the same boat as most, having only seen the movies, so I dont know this Ezra character, what i would say is that unless it is actually stated he invented the first lightsabre/blaster hybrid ever, it is entirely possible that is only the first one that has been shown in canon. 

I'm also confused about the argument that one has to be a force-sensitive to use a lightsabre effectively? To deflect blaster bolts, I fully understand. But in lightsabre on lightsabre combat it would seem to me its just wielding a hyper dangerous sword. I am by no means a swordsman, but i have sparred on occasion with friends who are (or as close as one can get in modern day, aka, fencing/Hema/kendo, yes they studied the way of the blade xD), and I've never hit myself, unless I'm doing something ridiculously stupid. Obviously an untrained individual would not fight effectively, but i see no reason a trained individual couldn't. Why someone unable to block blasterbolts would think engaging in cqc is a good idea I have no idea (in a large scale battle, I imagine a lightsabre would be a pretty good way to settle a random barfight).

Again though, i know next to nothing about Star Wars lore, each of my points may have a perfect explanation. If it is explicitly stated that Ezra invented the very first lightsabre/blaster hybrid, I would say one shouldn't break canon. I would also say I dont see any problem with saying that kills your interest, why roleplay if you cant roleplay what you want?

Albeit, the reply was curt, but perhaps they didn't want to argue further? Yes they were told it would be allowed if it had a sufficiently good explanation, but perhaps they thought wanting one was a sufficiently good explanation?

Just to throw it out there, I think an excellent explanation is that the owner thought shooting weakened blaster bolts that stun rather than kill, was more civilized than dismembering people at the least (heresy, i know). However being capable of wielding a lightsabre they recognize the utility and defensive applications, as well as the incredible power they can bring to bear should they have to. Assuming the character is not ambidextrous, being able to switch between the two without having to drop/holster one for the other would have obvious advantages. (I believe this was the reasonig behind gunswords as well) This argument would mainly be for force sensitives, and Jedi - primarily force sensitives, Jedi would more likely be capable enough with the force to incapacitate others through other means.
 A kind/wise jedi might feel that imposing ones will through the force to subdue someone was a violation of the individual. This would probably be a case by case basis: For a bounty hunter i doubt they would mind binding through the force. However an angry teen (pick a reason) might need to be stopped as well and dominating them in such a way would be an easy way to ruin any chance of reasoning with them. Getting shot by a blaster wont necessarily help either of course but it wont be someone wielding a power they barely understand to control them.

Again, I don't know nearly enough to give an actual educated opinion on this. I merely thought the discussion was interesting and wanted to share my thoughts, and potentially offer a solution for anyone desiring a blastersabre. My second explanation for Jedi may go against the Jedi code or w/e and be completely invalid interpretation as to how jedi view the force.