It's really more of a problem than just the BoVD. The real problem is that there is a wealth of contradictory precedent on the power of archfiends, and that people treat whatever precedent they feel like as "canon."
Others have (validly) stated that the notion of "CR" is a problematic one in 1e. However, one can reasonably talk about the kind of challenge that an archfiend as presented in the 1e MM would pose to a party of four 1e PCs. I'd say, on that basis (having, er, "playtested" the matter rather exhaustively in my younger days) that a party of 25th-level 1e PCs is quite capable of steamrolling Dispater, Geryon, Mammon, Belial, Juiblex, or Yeenoghu; Asmodeus, Demogorgon, Fraz'Urb'Luu, Graz'zt, Orcus, and Pazuzu (and to a lesser extent Mephistopheles, and an even [vastly] lesser extent Baalzebul) are harder. Orcus is actually easy due to his low hp, but try getting a player to put his character within melee range of the wand! Against a party with one or more +5 weapons, including a holy avenger and hammer of thunderbolts, and the insanely-high AC available to a fighter with +5 platemail and shield, plus a 25th-level wizard equipped with wish or time stop, any of the archfiends is toast. If the wizard can cast gate and summon a solar, the battle is a fait accompli, since none of the 1e archfiends is a match for such a creature.
Assuming, however, that the archfiend (per Deities and Demigods and Manual of the Planes) is treated as a lesser god AND is on its home plane, the battle gets much tougher. The fiend's hit points double, it gets access to some very powerful spell-like abilities, and it can summon allies with great alacrity. In essence, the fiend becomes equivalent to a 1e solar with (potentially) vastly greater hit points. Moreover, if the fiend has crafted a talisman, the PCs can't actually kill it; all they can do is prevent it from entering their home plane for 100 years or so.
So much for that. Of course, we now have the following to contend with:
1) The lesser god status granted to archfiends per Deities and Demigods. True, they have this, but archfiends (and Tiamat, Bahamut, and the couple of other entities sprinkling the MMs) are mechanically very weak for lesser gods. Only St. Cuthbert (who probably should be a demigod), Ralishaz, and a few demigods in DDG are on par with or mechanically weaker than the archfiends, even Asmo or Demo.
2) The "why don't the gods just kill the archfiends and take over?" argument that's advanced as a metasetting problem. This, incidentally, was constantly raised in Dragon magazine as early as I can remember. Gygax's solution was to just move all the deities out of the Nine Hells; the Abyss is plenty big enough for gods and demon princes alike.
As for the issue of high-level characters being much less likely in 1e: I'll sorta disagree. While it took *much* longer to advance in level in 1e than in 3e, there is full support for spellcasters up to 29th level, there is a Level X monster encounter table that features demon lords and archdevils, and there are XP awards for archfiends. I played PCs up to 30th level in 1e, and I know others who did also. There were NPCs of high levels as well; some of EGG's PCs were in the high teens, there was an archmage or two in the Greyhawk setting, and there was a demonstrated need for above-20th-level play as mentioned in the 1e gray box FR set, which featured above-20th-level NPCs.
