Just to quickly follow up with this.
Silver,
he listed the exact amount of time that is necessary for building the mana for a combo. It is a fact that you are casting more than you are sword comboing as a red mage. Its not just a preference, style of gameplay, or tailored to a specific encounter, red mage literally needs to cast more than it can do melee hits in all given encounters.
The mobility issues that individuals are talking about exist specifically within savage and ultimate content. No jobs, including red mage, have any mobility issues in the content outside of savage and ultimate raiding. To understand where people are coming from with the mobility gripe with red mage, you have to share their same experience- if you aren't doing that content, then yea, of course you can say that you have no issues with mobility, but that does not mean the class doesn't have mobility issues. It literally cannot do some of the mechanics because it's mobility is tied to its burst. Other jobs have utility that helps them move, we literally have to give up burst to move sometimes.