There's nothing wrong with burning BLU. I power leveled my BLU to 30, learned sandspin, got in a FC party, skilled up to about 15 or so in that FC party before I went afk for the night.
I woke up at level 99 the next day, learned pollen and afk skilled up while at work/sleeping, then went out and learned all the following spells:
Acrid Stream
Actinic Burst
Amorphic Spikes
Animating Wail
Auroral Drape
Awful Eye
Bad Breath
Barbed Crescent
Battery Charge
Battle Dance
Benthic Typhoon
Bilgestorm
Blank Gaze
Blastbomb
Blazing Bound
Blitzstrahl
Chaotic Eye
Charged Whisker
Cimicine Discharge
Cocoon
Cold Wave
Corrosive Ooze
Cursed Sphere
Dark Orb
Death Ray
Delta Thrust
Demoralizing Roar
Diamondhide
Disseverment
Dream Flower
Empty Thrash
Everyone's Grudge
Eyes on Me
Fantod
Feather Tickle
Filamented Hold
Firespit
Frost Breath
Goblin Rush
Head Butt
Heat Breath
Heavy Strike
Hecatomb Wave
Ice Break
Infrasonics
Jettatura
Leafstorm
Light of Penance
Maelstrom
Magic Fruit
Magic Hammer
Magnetite Cloud
Memento Mori
Mind Blast
Mortal Ray
MP Drainkiss
Mysterious Light
Occultation
Osmosis
Plenilune Embrace
Quadrastrike
Quadratic Continuum
Radiant Breath
Reaving Wind
Regeneration
Regurgitation
Sandspin
Sandspray
Screwdriver
Sheep Song
Sound Blast
Sudden Lunge
Temporal Shift
Thermal Pulse
Uppercut
Vertical Cleave
Whirl of Rage
Winds of Promyvion
Zephyr Mantle
These include all the proc spells and almost all of the spells that are useful today (missing Bloodrake and Tourbilion) plus probably an extra spell or so in there that's not useful (like Jettataru).
Anyway, in-between learning these spells, I camped the NMs for Almace, finished any AF3+2 gear I was missing, did a couple Sea runs to upgrade AF1 body to +1, and then over time I farmed/bought some gear for different gear sets.
So yeah I've only had the job unlocked for a few months now, but I have 5/5 Thaumas that I obtained all from playing BLU and I usually farm dynamis as BLU and make a little over 300 currency per run with a 2-boxed alt.
Nothing wrong with burning the job, as long as you take the time to read up on the job and understand how to play it, and then playing around with it a little to get the hang of it. I've probably read Prothescar's guide to Blue Mage about a dozen times or so. Read the Charged Whisker guide a few times. I've read through almost every BLU post on these forums (first few pages anyway) and asked questions about anything I didn't learn here. After that it was just a matter of getting used to playing the job. Like knowing what spell to use in reaction to certain situations. My first time in Nyzul it took me a while to get the hang of things, but now my group won't let me come on any other job. There are still a few things I could be doing better but I highly doubt that leveling the job on my own would have done me any good. It would've just been an annoying hassle and a huge waste of time.