If any of Henry IV's younger sons have offspring, it'll prevent much of the problems that lead to the Wars of the Roses. If there is tension between the Beauforts and the Yorks, it'll be people jockeying for position at court. That might lead to problems, but as well as the usual vying for influence, power and cash, the ultimate prize was on the table. York was the principle heir in the male line, before the birth of Edward of Westminster. But Henry's favouring of Suffolk and Somerset opened up the possibility that Henry could decide to put them into the succession, as heirs of John of Gaunt, even if everybody knew they weren't really legitimate. This tension was further exacerbated when Henry has his catatonic episodes.
In TTL, that additional tension isn't there. The son(s) of Clarence/Bedford/Gloucester* would be the undisputed heirs prior to the birth of an *Edward, if it happens in this TL. Moreover, the same heir would be the obvious Lord Protector/Regent in the event that Henry has a similar fit of... whatever it was.
*Not entirely sure it matters which one. Bedford's the better role model for one of them to follow, but Henry VI was the son of Henry V, so that's not useful guide. Whichever it is, he's the senior adult male prince of the blood, and heir until Edward, or an analogue, is born.