I have serious concerns about the accuracy of that last parse. For starters I'd want to know crit rate (should be around 5% if they were only using rains, separate the pets, otherwise it will take those into account). I'd also want to know whether monster summonings and/or host of the elements was used (many raid encounters they are next to useless due to ae's and whirlwinds fucking their face right off). I'd also like to know why and how your warrior was doing competitive dps with the mages and rogues. I'd also like to know why there are 4-500 less hits on the rogue than on the warrior. I'd also like to know why your wizard was only engaged for 57 seconds (I'm assuming death).
Mages provide:
1) Mana to the raid
2) Fire resist to the raid
3) A serious FR buff or whatever to the caster/xyz group
4) Mad fucking pet summons
5) Peridots, the mechanic that exclusively revolves around mages as much as I hate peridots you need a fucking mage to make them happen.
6) loot bonus
Rogue provides
1) 300 more dps
Modrods and loot bonus are the only things they need to actually be there for that are of value. Elemental barrier is way too short (in addition to being situational) to be more than a blip on the radar. Other than that mages are basically vending machine buffbots, and the buff is situational, replaced easily by a competing buff when fire resists are not needed.
Also, those are some of the reasons they are exceedingly poor for 6man groups, including their dependence on others to keep their pet alive. That and only having two types of worthwhile damage to choose from (fire and magic)( the lure, is a dd, pitiful, and extremely expensive. As well as being completely unnecessary) pretty much kills your dps in places like emberflow and tot, leaving you to rely on relic rain and your level 60. With magic immune or extremely resistant areas you fare even worse, getting to rely on archaic and sirroco, which you may remember from level 55.
As far as nonraid content, if one is going to have to drag a healer around everywhere as a mage (which one pretty much does). You may as well just play a class that is going to do comparable dps, and allows you to do far more difficult things.
As for the earlier levels, I remember quite a bit, but I really don't feel like rehashing things any more than I already have. Like that 20 level stretch where you're stuck with a 100 hp petheal.
Tldr; A healthy proportion of mages move on to classes without the glaring downsides of blowing over in a strong breeze, blasting yourself in the face a bunch, needing to loaf on your ass every few minutes in a group, and being so incompetent with pet care it's a wonder the elemental spca doesn't show up every 30 minutes with a massive fine. I went with two healers the majority of the time before I quit (apart from raiding), was much happier with them.
Sidenote: I don't think a hot is the way to go. A direct way to boost the pets damage is all well and good, but adding a hot will just end up making it cost more, be worse, and lose out to better spells on the bar. We especially don't need more healing with a recast.