OK, you're right. From p B13, under the heading
Inheritance:
If the DM wishes, a player may name an heir to inherit his or her worldly possessions upon the death of the character. The local authorities will, of course, take 10% in taxes, before giving the inheritance to the heir. This heir must always be a newly rolled-up first level character. This "inheritance" should only occur once per player.
That last sentence is confusing, to me at least. Does it mean each player may have only one heir for his/her PC at a time? That each heir can inherit from only one player's dead PC? Or (the weirdest reading but the most natural literal take on the words) that there is a lifetime player limit of one inheritance, no matter how many PCs you play and lose?
Consider The Basic Set as a contained unit. So you've got a singular Town, and characters are only leveling up to 3, and you're going to have maybe 7-10ish Scenarios for the players to scout out and pick and choose adventuring sites from in the course of maybe 10-12 sessions of play?
So a single Inheritance per player under that paradigm is pretty much on the mark.
Including Expert and Companion play, we refreshed Inheritance at 4th and 16th. Characters (obviously) get extremely stout at that point.
Here is Moldvay on alignment (p B11):
Players may choose the alignments they feel will best fit their characters. . . . The alignments give guidlines for characters to live by. The characters will try to follow these guidelines, but may not always be successful. If a DM feels that a player is not keeping to a character's chosen alignment, the DM may suggest a change of alignment or give the character a punishment or penalty.
I think this is pretty similar to how Gygax presents alignment. It is "prescriptive", not merely "descriptive", establishing in-principle constraints on action resolution. Because they are only "in-principle", players can violate those constraints, but adverse consequences might follow.
So choosing alignment is also specifying an aspect of the role the character will fill - hero, roguish scoundrel, or villain. (I have doubts that 9-point alignment is very useful for this, but I don't think Gygax fully thought that through in terms of the changes it would lead to in relation to alignment as an element of the game.)
My take that Alignment in Basic is mostly (but not wholly) a superfluous component of play is underwritten by these lines of evidence (of which I suspect you disagree!):
1) The game is centered around dungeon exploration and treasure hauling. Mechanically, the game is systemitized around this premise. Importantly, this is only accomplished when performed as a cohesive, versatile unit with requisite supplies/retainers, correct marching order, and sensible actions taken during Exploration/Encounter Turns and during (what Torchbearer would call) "the Town Phase."
Most all folks hew to generic Lawful or Neutral play, because legitimate Chaotic behavior (Kender-like as depicted) damages prospects for success in the following ways:
1a) Dysfunctional Exploration synergy (leading to needless resource loss and needlessly assumed risk).
1b) Dysfunctional Encounter synergy (leading to needless resource loss and needlessly assumed risk).
1c) Mistrust and lack of dependability sows player morale issues (which feeds back into a and b).
1d) Poor reputation in town contracts prospects for adventuring sites and...
1e) Negatively impacts Retainer retention.
2) The nature of the party Caller funnels group action declarations towards something coherent or at least works as intermediary when there are disputes (diminishing the frequency and impact of spikey, reckless, weird action declarations)
3) Unlike AD&D and 3.x, nothing mechanically interfaces with Alignment.
3a) There are no Barbarians, Bards, Druids, Monks, Paladins. Clerics are merely forbidden from using edged weapons (no ethos dictates/constraints).
3b) A stray few spells interface only with Evil (none interact with Law, Neutral, Chaos).
3c) Traps are of the martial/mechanical variety. No runes/glyphs of warding against Law, Neutral, Chaos.
3d) Magic items don't interface with Law, Neutral, Chaos.
3e) Monsters (again outside of the unique language - which is certainly relevant in play and why I called it out above) don't interface with Law, Neutral, Chaos.
4) Alignment doesn't interface with the Monster Reactions table.
5) There is no xp feedback...while there is one for Prime Requisite. Contrast with Torchbearer's dynamic feedback with Traits and Nature or Dungeon World's Alignment and Bonds. Modvay Basic could have trivially accomplished making Alignment central (rather than imo mostly superfluous) merely by mapping Alignment's impact to Prime Requisites. Have 3 questions for each Alignment. At the end of each session, the group reflects on the play of each PC to see if they fulfilled one of them in a meaningful way. Yes? 5 % xp bonus!