I'm curious, the book says that most Space Marines that enter the deathwatch are experienced enough to have passed through all the stages of Space Marine training, from heavy gunning, assault and finishing with Tactical. Then, why only the assault marine specialization can 'use' the jump packs? Specially since, to become a Tactical Marine, you have to pass through Assault Marine phase? Assault Marines are the only ones who can buy the "Pilot (Personal)". I figured that all Astartes would be able to use Jump packs when needed, but only Assault would be able to do twirls and special jump attacks. And sincerely, I'd be up to let my players use jump packs if they have the requisition for it, but only Assault Marines to be able to do astounishing feats of assault-jumpery.

Apologies, I missed the "Pilot (any)" on Rank 3 of the General Space Marine Advances, though my question still stands, why can't a space marine start with such skill, if it is both in the common lore -and- the book that all space marines are trained in the assault role?

I would say that it is due to the Assault Marine speciallizing after going through all of the trials, making him more efficent with the Jump-Pack than the other Marines.

After all the Deathwatch consist of Marines which are experts in every area, but later still speciallizing on a certain aspect to be super-superdeadly.
But that's just my explanation

Exactly, this translates in game with the capability of any astartes to use weapons from 'other specializations', for example an assault marine picking and using a heavy bolter, or a devastator using a power sword. But nothing is said about the jump packs.

(Also is it just me or the servo arm of the techmarine is barbarically overpowered?)

The Errata (on p. 2) added the Pilot (Personal) skill to Rank 1 on the General Space Marine advancement table, and set the cost to 100 XP. You're right, it would still make better sense to hand it out with the other beginner skills, but still, it's laughably cheap and easy to get it if you desire to do so.

I've seen the Errata, indeed it's there!

(Also is it just me or the servo arm of the techmarine is barbarically overpowered?)

It's pretty strong in early to mid game, but on the other hand, most tech marines don't have the easiest time hitting the garage door in front of them.

I mean, that monstrous arm literally does more damage than the Omnissiah's axe! The only disvantage in using it would be if the Techmarine found a foe with a power weapon!

2d10+14 or 2d10+16 Pen10 are nothing impressive for melee to be honest. Its only boon is the attack for an reaction and that can be utilized quite neatly.

Also the Omnissiah's Axe deals 2d10+5 Pen6. Lets take a rather standard marine with 50 base strength and a regular Power Armor with "just" +20 strength and the Axe deals 2d10+17 or 2d10+19 Pen6 if MC.

In terms of maximizing melee damage, if that is your thing, both options are far from optimal.

I mean, that monstrous arm literally does more damage than the Omnissiah's axe! The only disvantage in using it would be if the Techmarine found a foe with a power weapon!

Well, it's a ******* mechanical arm (I mean, just have a look at the picture). It has a Strength value of 75, counting as Unnatural Strength(x2). Taking that out of the calculation, it leaves 2W10 Pen 10, which isn't even close to OP (see FieserMoep's post). Especially if you consider that a good part of pen 10 will be unused in 90% of the combats.