I'll answer for James, as I'm most familiar with his parliamentary dealings.

First, I think you're simplifying the idea of what it means to be an absolutist. James I did not have the level of control over his people that Louis XIV had - James would never had said L'Etat, c'est moi (I am the State). James wrote extensively on his power as King and the more important element was that he ruled by Divine Right, not that he had absolute power. I think you are coming to this from Sommerville's Politics and Ideology, which has been challenged since its publication by a few works, including Glenn Burgess, The Politics of the Ancient Constitution and his Absolute Monarchy and the Stuart Constitution.

There were two main reasons for James to pack his parliaments. The first was that in his entrance into England, James was a foreigner. He was a Scottish King attempting to take over from and English Queen. James did not have the power or the support in any sense to just do whatever he pleased. James was an astute political observer and he knew he had to govern by consent with parliaments in order to govern at all. It was only after the failure of his "Great Contract" in 1610 that James tried ruling without a parliament for a significant amount of time (Russell, King James VI and I and his English Parliaments, chapters 2-5; Young, Search Results King James & the History of Homosexuality, introduction).

The second item is that English Kings could not tax without (parliamentary) consent. English Kings could levy money without the consent of parliament, and this was a large part of the king's prerogative. The two major types of levies included forced loans (Amicable Grant of Henry VIII, Forced Loan of Charles I), and the collection of customs duties. These were an inherent part of English Kingship because they were either a personal collection of money to be repaid by the King (not the state) in the case of a forced loan, or were part of negotiations and diplomacy with foreign nations (Mark Kishlansky, "Charles I; A Case of Mistaken Identity' Past & Present (2005)).

I understand where your question is coming from, but the thing to consider is the difference between political theory and political reality (Burgess, Absolute Monarchy, pp. 17-19). In theory, Kings had enormous discretion in how they could exercise power. In reality, kings were restricted by the political world they lived in. James would never have been a successful monarch had he not attempted to work with parliaments throughout his reign; the elite and country at large would never have stood for it. Charles, despite his problems, almost always tried to ameliorate his positions when he found that the implementation of his policies met strong resistance. Secondly, kings were restricted by God's law. That sounds foolish to modern ears, but it was a real restriction in an age when King's believed their authority was derived from God and that they would be held accountable for their actions by God.

There were aspects of their prerogatives that the Stuart kings were unwilling to compromise, but when it came to the implementation of things like religious uniformity, they were willing to be flexible (note - religious uniformity in the sense of things indifferent. They were much more strict on specific theological points like transubstantiation).