Considerations of armorial designs including straight-line per-pale or quarterly field divisions often include a discussion of whether they have “the appearance of marshaling.” Putting aside the question of how we answer that question (already ably addressed elsewhere, see here and here), one might wonder why this is an issue — why doesn’t the SCA’s College of Arms register armory that has the appearance of marshalling?
I believe the answer is that marshalled arms were not issued as such by period heraldic authorities, nor did newly-armigerous families assume already-marshalled arms.
Instead, each individual coat of arms was granted (or assumed) independently, and it was only after that point they were ever combined via impalement or quartering (or sometimes more esoteric arrangements as seen in Iberia).
A heraldic authority might confirm that a particular individual had the right to display each of the individual quarters, but they were still separable, and (for example) a noble might split their titles and lands between two offspring, who would each inherit the armory associated with specific estates, in a process we might think of as “un-quartering.”
It’s possible that there were occasional exceptions to the above principle — for example, Birgitta Lulli, Pelican emeritus, reports that in post-period Scandinavia, some nobles adopted new coats with quarters that had not been independently granted, in an effort to make themselves seem of equal status to older families which bore quartered arms — but I haven’t ever encountered any period examples of arms being granted in already-quartered form.
An individual either has rights to each particular coat or does not; once they have secured those rights, it’s up to them as to whether they impale or quarter them, or display the one they think is most prominent and ignore the other, or display one in one place and another elsewhere, or whatever they’d like.
Therefore, if you want to display arms that have the appearance of marshaling, you must register each individual design, after which point you are free to display them together, pass them on to your heirs, and so forth. (Just like in period, where if you wanted to display the arms of Savoy quartered with the arms of Loraine, you had to first achieve the lordship of each territory, at which point you could fly them together.)
This policy has been in place since the early years of the Society, when Ioseph of Locksley, second Laurel Herald, wrote in the June 1973 LoAR that “… it is the policy of the Imperial College to register the individual parts of marshalling rather than the full marshalling itself… Let [a couple wishing to display marshalled arms] submit individual applications and emblazons [for each part].”
[January 2023 — Edited to add:] An Iberian example of seemingly-quartered arms was recently circulated, dating to 1524. Nonetheless, these examples are rare, and appear late, and are not the foundation of our practices.
[December 2023 — Edited to add:] Notably, the examples of late-period armory which was granted with the appearance of marshaling was specifically designed to give the appearance of marshaling — eg, it was not just an independent stylistic decision considered to be a standard part of the heraldic design space, but rather an exception to the rules and an explicit attempt to grant the appearance of old nobility to a recent arriviste.