The only time I find prior label links to be of use is when they have a dedicated band page with a bio and stuff.
For instance, take the band Gardenian. Their debut was on Listenable, and their other 2 albums are on Nuclear Blast. The band is dead, and there's no official homepage, and Nuclear Blast sadly has no page dedicated to that band. Yet, Listenable DOES have a page for them, which is strange. But at any rate, I consider such an example very useful.
If a prior label has no dedicated bandpage, or the band is not listed anywhere on the site, then IMO it should NOT be linked. If it is in the label's page (with some info), either as a dedicated bandpage or in an alumni section or whatnot, then I think its ok to link.
From my experience, some labels (like Noise) have a fair amount of info on their old bands, while some other labels like Century Media drop their old bands like a bad habit. Ultimately, I think it comes down to the users best judgment here. Ask yourself: "does linking this label provide any useful information to any fan of the band investigating the band's page on M-A?" If so, then link it, if not, then there's no point in really bothering.
One thing I have noticed, is some labels issue, reissue or distribute albums, but have minimal, if any info on the band (this is far more common in black metal). Should such entries be in labels or merchandise? Also, what about licensees? For example, bands like Sonata Arctica, Children of Bodom, and Nightwish have always been originally signed to Spinefarm, but licensed out to labels like Nuclear Blast, Century Media, Roadrunner, etc. Should the licensee labels still go under labels? (Personally, I'll only add such labels if they have info on the band, like a bio and whatnot)
Also, there's instances where labels from Russia (eg, Irond) and Japan (eg, Spiritual Beast) license a band's material. The only circumstance that I will ever add such a link (to labels, of course) is if it is in English (I have seen a few rare cases where such a link actually provides some useful info).