Wills do in fact exist in the world of Westeros. And more specifically they’ve been plot points in regards to chosen heirs. Robb Stark has an entire debate with Catelyn about choosing his heir. Sansa is ostensibly his heir with Bran and Rickon considered deceased. And yet Robb and Catelyn believe they can skip over Sansa by naming another heir. Why would they believe this possible if there isn’t precedent for a King choosing his heirs ?
“Young, and a king,” he said. “A king must have an heir. If I should die in my next battle, the kingdom must not die with me. By law Sansa is next in line of succession, so Winterfell and the north would pass to her.” His mouth tightened. “To her, and her lord husband. Tyrion Lannister. I cannot allow that. I will not allow that. That dwarf must never have the north.”
“No,” Catelyn agreed. “You must name another heir, until such time as Jeyne gives you a son.” She considered a moment. “Your father’s father had no siblings, but his father had a sister who married a younger son of Lord Raymar Royce, of the junior branch. They had three daughters, all of whom wed Vale lordlings. A Waynwood and a Corbray, for certain. The youngest... it might have been a Templeton, but...”
“Arya’s gone, the same as Bran and Rickon, and they’ll kill Sansa too once the dwarf gets a child from her. Jon is the only brother that remains to me. Should I die without issue, I want him to succeed me as King in the North. I had hoped you would support my choice.”
We also know that even lords can also seemingly choose their heirs and even have stipulations for those heirs. Why ? Because it’s actually a plot point in The Sworn Sword. Rohanne Webber (Tywin Lannister’s paternal grandmother) is her father’s named heir but there’s a stipulation, she has to be married or she will lose her rights to inheritance and it will instead go to her cousin Wendell Webber:
“Her lord father’s will demands it. Lord Wyman wanted grandsons to carry on his line. When he sickened he tried to wed her to the Longinch, so he might die knowing that she had a strong man to protect her, but Rohanne refused to have him. His lordship took his vengeance in his will. If she remains unwed on the second anniversary of her father’s passing, Coldmoat and its lands pass to his cousin Wendell.”
How is that a possible stipulation that Rohanne takes extremely seriously if not for the fact that inheritance is not clear cut and can be overridden by a will ? And this evidences further that a Lord or King can choose their own heirs.
Maegor disinherited Jaehaerys and made Rhaena’s daughter, Aerea, his heir.
Jaehaerys went against Andal inheritance tradition to pick Baelon over Rhaenys.
The lords at the Great Council doubled down on that decision by picking Viserys over Laenor which Jaehaerys upheld.
Aegon III’s regents pick Rhaena as his heir over Baela, despite the fact that Baela is the elder twin, because she’s too willful and wild and won’t accept a marriage pact they made for her.
Jeyne Arryn picks a distant cousin to be her heir instead of a closer relative with more traditional claim, the King’s regents back her decision.
Aerys II picked Viserys to be his heir when Rhaegar’s son Aegon was the traditional choice.
Doran Martell planned to make his son Quentyn his heir because he wanted his daughter Arianna to be queen conosrt of the Seven Kingdoms, she doesn’t know this and just assumes he’s pick Quentyn over her.
Walder Frey talks about picking his unborn son as his heir over his dozen or so adult sons.
Rodrick Harlaw offers to make Asha his heir to stop her from participating in the Kingsmoot.
Stannis offered to make Renly his heir instead of Shireen.
You will love this video by the former ozymalek, anon (now they are Youtube and Tiktok's "PhoenixAshes"). It basically speaks of exactly what you emphasize for Westeros--how heir voluntary designation was a real thing in real medieval Europe.