Maybe too broad a question, but why were already-wealthy-and-powerful medieval lords’ so eager to enter the dangerous waters of politics for their advancement? I.e. the wealthy and powerful Boleyn’s scheming to marry Anne to Henry VIII; isn’t it a bit like a multi-millionaire gambling with the Mob to see if he can become a billionaire?

Well, to quote the Boss:

“Poor man wanna be rich,
Rich man wanna be king,
And a king ain’t satisfied,
‘til he rules everything.”

To take your Boleyn example, the Boleyns weren’t actually all that rich and powerful. Thomas Boleyn, Anne’s father, was the son of a wealthy mercer who had bought himself a knighthood and a marriage to a Butler of Ireland. That still made him relatively low-ranking, a mere knight and diplomat, despite his incredibly fortunate marriage to a Howard. But through Anne, Thomas became Viscount Rochford, Earl of Wiltshire, and Lord Privy Seal. So for the upwardly mobile, politics offered an opportunity to join the true elite. 

For those already there, there’s always more to get. The Kingmaker was born the son of the Earl of Salisbury, but marrying Anne Beauchamp got him the Despenser fortune and through some rather complicated legal maneuverings, the Earldom of Warwick, which was to be the foundation of his empire. The Kingmaker sided with the Duke of York in part because Somerset (the leading Lancastrian) had taken the Lordship of Glamorgan, which had been part of the Despenser legacy. Siding with the Duke of York got him the position of Constable of Calais, and siding with Edward IV got him the Admiralty of England, the Stewardship of the Duchy of Lancaster, his brother got made Warden of the East March and Earl of Northumberland, and his other brother got the Archbishopric of York and the Chancellory of England. 

But there’s also the fact that in feudal politics, most of the time, everything belongs to someone. So a lot of people stayed in the game to avoid losing what they already had – the losers in a civil war, or even the people who weren’t friendly enough with the regime, could lose Dukeships, Earldoms, and Baronies aplenty.