The time it takes to learn spells can't really be an argument for BLU's strengths/weaknesses. I must admit that's a weak defense. Mages don't get to complain about the high cost of spells they paid for years ago and even some today.
You can say "I could do it in a week" (get all the spells/gear/macros), but it's probably harder than you think it is and it depends on what you define as "gear" and how much you're contributing to the fight. Are you getting friends or your main to carry you, or are you going out there in sparks gear and fighting through Escha NMs and easier versions of Ambuscade? If you're getting crazy assistance, anything can be geared in a week.
Edit: It also depends what you mean by all spells. Sometimes, even with diaga or blugeon spam, getting the mob to tp and use the spell you want it to and winning the RNG game of learning the spell can be rough. Battery Charge and Self-Destruct were awffffullll for me. Some were hard, some weren't, but those two were the worst.
A lot of the spells are irrelevant for actual use, but equipped because they cost less Blue Magic Points to achieve the same tier..
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I would say BLU is a bit more difficult than most melee to gear.
You need varying levels of TP sets (low/mid/high acc), dt sets, multiple ws sets. All this applies to every melee. You need Fast Casts sets (technically applies to every melee except probably sam, mostly NIN, RDM, DRK, BST, Other jobs for /nin, but nin isn't that useful anymore). Need a skill set (applies to DRK, RUN, RDM, NIN). You need an MACC set (DRK, RDM, NIN--butlol). BLU needs a healing potency set.
BLU doesn't "need" a skill set any more than RDM "needs" an enhancing set or a duration set. Dedicated BLU/RDM will have it, others will not. BLU not having a skillset will probably be more punitive on the BLU.
No offense but I'm being really generous including RDM in these lists. I should list PLD before I list RDM.
BLU should have idealized sets for preferred physical spells, but this isn't 2008, your primary source of physical damage is how fast you can get to 1k TP and what you can do with that, especially stacked with other melee that TPing right along with you. Try to CDC>Sinker Drill? You won't get the MB off before someone else has ws'd something. Hopefully it's rudra's.
Highly skilled and highly dedicated, BST probably can still solo things that equally-played BLU can't. BST still does probably have maybe the most amazing 1hr in the game. It's also probably true that BLU might solo things BST can't. I've said before, I don't play this game to solo.
We can talk and talk about why BST was nerfed but when you look at what the change actually affected, the answer is clear: BST could stand at max range and do maximum damage, safe from most enfeebles/aoes and at the bare minimum of enmity. I've always agreed that the distance is restricted too far, but the distance needed restricted. BST didn't get nerfed because of its AOE capability because that remains exactly as good as it was in cleaving XP and in boss fights.
I can't really think of any mechanic in any fight that BLU can just ignore either. Yes, we can erase debuffs and reapply Haste, if we set an erase to do that (losing some other spell, thus losing DPS), or sub dancer, white mage or scholar (blu/dnc is gross, blu/whm is, and blu/sch is for melee). Those same options are also available to other melee. Trusts can do it, virtually any whm trust will, but you can't frame a balance discussion around what trusts can do.
When BLU does sub dnc, it loses any respectable offensive ability. All it has is Chain Affinity, Burst Affinity, and Efflux. It gains the same weaker Reverse Flourish every job /dnc has. BLU's 2hr's are also pretty lackluster compared to most DD/Pet DD. It gains Dual Wield but thankfully, gifts don't amp up traits that subs give. You either go with the slower attack speed or you work with usual spells. Alternatively, you can gear more DW+ and otherwise lose DPS from the multi-attack/store-tp gear that you're wearing. Of course, 5% from Haste Samba is worth mentioning.
We can talk about BLU's ability to delay cap, which is beneficial to every job, but most DD have their own traits that people don't consider. In a party with an RDM, SMN, BRD, Frequently GEO (there are often times your group just doesn't need anything else), or another BLU, the value of BLU's DPS enhancements (delay reduction) falters (For the fights that last long enough/spammed, MG is nice from a second BLU).
None of BLU's offensive abilities affect how hard it WS's. Nature's Meditation (atk boost) does and Tenebral does (difficult to land on things worthwhile. If you have a geo, it's probably not even worth using). BLU's strength comes in from the traits it can set (Triple attack, Critical Attack Bonus, Store TP, Skillchain Bonus), but all of these things are applying towards a blank slate.
I can share some sort of delay reduction with you, you can't share your abilities with me.
I realize people are pretty set in their own opinion, and this won't sway anyone, but it was worth stating.

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