The first sentence at Chief Baron of the Exchequer
The Chief Baron of the Exchequer was the first "baron" (i.e., judge) of the English Exchequer of Pleas.
bemused me: Why were these judges were called "barons"? I looked it up on OED:
The list of all Barons of the Exchequer is incomplete. So I'll refer to the list of Chief Barons:
In the screenshot, nobody were barons except Lyndhurst. So why weren't the (Chief) Barons created baronies? It feels uncomely to be Barons of the Exchequer but not "true" Barons, though I know that UKSC justices are no longer created baronies but remain styled 'Lord' or 'Lady'.
The short answer is that the members of Court of Exchequer were called Barons because that was members of that court were called.
The answer is that the titles and court were created in the 1190's when there was no such thing as the House of Lords and titles were not regulated as they were later. To show that not all Barons are in the House of Lords. Wikipedia says
Under King Henry II, the Dialogus de Scaccario already distinguished between greater barons, who held per baroniam by knight's service, and lesser barons, who held manors. Technically, Lords of Manors are barons, or freemen, however they are not entitled to be styled as such. John Selden writes in Titles of Honour, "The word Baro (Latin for Baron) hath been also so much communicated, that not only all Lords of Mannors have been from antient time, and are at this day called sometimes Barons (as in the stile of their Court Barons, which is Curia Baronis, &c. And I have read hors de son Barony in a barr to an Avowry for hors de son fee) But also the Judges of the Exchequer have it from antient time fixed on them."
The same article continues to say that after Magna Carta the greater barons were summoned to the King's Council which evolved into the House of Lords (and the current definition of Baron) and the lesser barons were summoned by choosing members fo a group of them eventually this became House of Commons.
Thus in Norman era pre 1200 Baron was really just a term for those who had sworn fealty to the king.
"Select Charters and Other Illustrations of English Constitutional History from the Earliest Times to the Reign of Edward the First (Cambridge Library Collection - Medieval History)" By William Stubbs Amazon.co.uk Google Books shows
The several members are called… in the Exchequer barones or barones scaccari, a title that belongs to them even after they have ceased to be chosen from the ranks of the great vassals.