The point of the Speed Factor variant is to make combat more unpredictable by varying turn order. From the DMG (p. 270):
Under this variant, the participants in a battle roll initiative every round.
Many actions--particularly spells, but also melee attacks like a monk's stunning blow--produce effects which last until the actor's next turn or impose a penalty on the opponent until the opponent's next turn. (Depending on the effect, it could be start of turn or end of turn.) But these rules seem to be designed to work with a fixed order of initiative, so that a combatant or an opponent gains the benefit or suffers the disadvantage for one turn.
If turn order can change from round to round, however, a character could cast a defensive spell on a low (late) initiative roll, then get a high (early) initiative roll the next round, have the effect expire, and never actually gain the defensive benefit. Conversely, a high (early) initiative roll followed by a low (late) initiative roll could give the character the benefit against two rounds of opponent attacks. Similarly for effects or conditions imposed on opponents, which might actually have no effective duration or twice the effective duration.
Since Speed Factor is a variant rule, I don't think there is a RAW answer (beyond "Them's the breaks"). Therefore I am interested in answers that include elements of the following:
- Statements from authoritative sources (Sage Advice, other communications from game designers).
- Rules as interpreted with evidence from the sourcebooks.
- Actual experience in play, particularly if you have tried different approaches.
- An evaluation of the impact of rules tweaks to reduce or otherwise handle the wide swing between no effect or double effect for effects that are supposed to last for one combatant's turn.
Note: A previous question about the variant initiative rules asks when to trigger certain class features (e.g. the monk's Perfect Self) that normally trigger at an initiative roll, given that under the variant rules initiative is rolled several times per encounter. The answer was essentially those features should trigger once at the beginning of the encounter. My question is about any effect that is measured in turns during combat (but especially those with a duration of 1 turn), and the answer to the previous question cannot be sensibly applied in this case.