Show me a game in the series where RDM's melee attacks were a real 'thing' vs just 'they can use a weapon and their attack isn't completely useless. They weren't even that great at melee in FF1!
It's clear though their inspiration is from FF5's design, where RDM was more about spamming spells fast than being a stabwizard. (Contrast with Mystic Knight, the actual 'melee and magic job')
And the argument isn't 'fun', it's in unnecessary convolution. The BGoT problem isn't one of 'fun', it's of annoying convolution. Turning RDM into a melee doesn't make it a better fit for the role it has, it makes it unnecessarily convoluted (and is detrimental to its place in savage content)what one finds "fun" may not be "fun" to others.
When I look at proposed changes, I look at how it's going to change how I do content. I look at things like Light Rampant, or Add Phase in E8S. I look at how this would feel trying to deal with hard mechanics--and a lot of it does not assist that.
RDM doesn't need a DoT to manage, because that doesn't help its gameplay. RDM doesn't need scuffed balance guage add-on, because that doesn't help its gameplay. RDM doesn't need a 6th burst combo, because that doesn't help its gameplay.
Instead, look at what painpoints actually exist in the class that are universal (not just 'I want a gish so change RDM to cater to me only') but things everyone agrees affect the job.
1) RDM needs a defensive cooldown other than Addle. If that 'something' is 'Titan-egi is deleted and manawall is now a role action' I'd be happy with that.
2) RDM could use (but not necessarily needs) a way to get out of the situation where it's overproc'd going into melee.
3) Maybe a resource that builds off your physical ogcds, that you can spend on a physical attack, kinda like a RDM-variation of Shoha. It'd do big potency and it'd look cool.
4) A nerfed version of Lost Chaincast, that ability is an RDM classic and way too damn fun. That's your level 90 keystone right there.
5) Upgrading Verthunder and Veraero in a trait at EW launch instead of waiting for patches that end up just doing that anyways... again.