First: I think we have to differentiate the
"soft" burnout where you just reduce your magic rating to 0 from the
"hard" burnout, where you lose more than 5.0 Essence points and thus reduce your max. magic to 0. Even in 6th Editions RAW, you canīt get your magic back in this case, so itīs practically permanent. Well, one caveat here - it
is possible to initiate first and thus raise your max. magic to 7. This basically means that an Initiate canīt really suffer a "hard" burnout.
But IMO, the real problem here is not so much that you can still "rediscover" your Magic after a burnout of either kind.
Itīs how cheap it is: Just 5 Karma to go back from 0 to 1. At least thatīs what people assume (is there some official statement? Probably. The worse the rule, the easier it is to get an confirmation by CGL

). And apparently, it doesnīt even matter what your "starting magic" was before the Essence loss occurs: You can start with Magic 1, load up with 5 points of Cyberware for an almost complete burnout and you still just need 5 Karma to bring back your magic abilities. Sure, you are stuck with a max. magic of 1, but a few Initiations and some Foki go a long way here; and if you go for an Adept build, you can just stick to powers that donīt care about your magic Attribute. In the end, you lost almost nothing besides 5 Karma and the nuyen for the Augmentations.
It doesnīt have to be that way. When I started playing SR back in 4th Edition (where you would suffer a "hard" burnout whenever your magic dropped to zero, BTW), we always assumed that the Essence loss doesnīt just reduce the Magic Attribute, but also imposes a kind of permanent debuff on it. To reflect this, we noted the effective Magic Rating in Parantheses on the Character sheet, like you would with augmented values as well. So, when you are at Magic 3 and lose 2 points of Essence, your Magic isnīt noted as 1, but 3[1]. Subsequently, buying back those 2 lost points doesnīt cost you the 10+15 Karma to go from Magic 1 to 3, but 20+25 to go from Magic 3[1] to Magic 3[5]. Thatīs arguably a much more significant investment. And the aformentioned "burn out & buy back" cheese would be immensely costly: Instead of buying back your lost Magic 1 for 5 Karma, you had to raise your Magic from 1[-4] (treated as Magic 0 for all purposes, the notation is just a reminder) all the way up to 6[1] for a whooping 10+15+20+25+30=100 Karma.
Iīm not sure if this interpretation was correct back then, but it kept being our preferred houserule all the way down to 6th Edition. I really found this the best way to handle things from both a balancing and the "burning out is pretty bad, Mkay" lore perspective: Itīs not entirely impossible to regain your magic after a massive burnout due to augmentations, but it takes a lot of dedication. So much that it makes sense if most burnout Mages just give up on the way.
Hell, compared to paying 5 Karma to get your Magic back,
that could even make for a great narrative arc
