This may sound unintuitive, but a new kingdom could not be trivially proclaimed. Calling yourself a king has very little meaning if it isn't recognised by anyone else. For maximum acceptance by your peers and subjects, therefore, your new kingdom had to be properly constituted by the lawful authorities.
In the case of Latin Europe during the High Middle Ages, the creation of new kingdoms was considered the prerogatives of the Pope and the Emperor of Christendom.
So high were the notions of this great monarch, in an age when the privilege of creating new kingdoms was deemed to belong only to the pope and the emperor.
- Hallam, Henry. View of the State of Europe during the Middle Ages. Vol. 1. Harper & brothers, 1853.
Therefore, Baldwin of Boulogne was not legally empowered to simply declare himself king. Nor is there reason to believe that either the Pope or the Emperor would have supported him in creating a new kingdom. Constitutionally speaking, making Edessa a kingdom was a non-starter.
Now, he could say to hell with it and style himself king of Edessa, but no one would respect that. As a mere son of a count in Europe, his takeover of Edessa was through rather questionable means. When the crusaders were electing a king for Jerusalem, he was neither their top nor second choice.
With neither political nor popular support, the diplomatic reality of the time made creating himself a king untenable. Especially because it would surely set himself up for conflict with Jerusalem.
That new kingdoms had to be created by Imperial or Papal authority was a very well established legal doctrine. A contemporary example of similar circumstances would be the Crusader kingdom of Cyprus, created by Emperor Frederick II.
The creation of a new kingdom was not, in the Middle Ages, a casual act. Brand new kingdoms, such as Sicily, Cyprus, or Armenia, were constituted by popes or emperors in the twelfth century. So the question arose, when a new kingdom was created, whether the western emperor approved the pope's creation, or vice versa.
- Abulafia, David. Frederick II: a Medieval Emperor. Oxford University Press, USA, 1988.
Perhaps the most famous case is the failed scheme of Charles the Bold, the powerful Duke of Burgundy, to create a kingdom for himself. He attempted to do so by securing the sanction of Emperor Frederick III, but his boldness ultimately derailed the effort.
Frederick and Charles met in Trier in 1473. Although the emperor declared that he was prepared to bestow the status of kingdom on a duchy ... Charles held out for more, demanding that he be put forward for election as the Roman-German king, and hence as successor to the office of Holy Roman Emptor, and this led to a split. Frederick left the duke without any formal farewell.
- Fried, Johannes. Das Mittelalter: Geschichte und Kultur. CH Beck, 2008. Translated by Peter Lewis.
Another example comes from Scottish jurists during the Union of the Crown. Here we see the doctrine being connected to divine rights, with kingship compared to baptism.
But the power of creating new kingdoms belongs solely to the Emperor and the Pope. It is unknown to any constitutional system, indeed is altogether impossible for a king to create himself, to confer authority on himself, to be the author of his own prerogative; for no king can act beyond the power which God has conferred on him.
- Craig, Thomas. De Unione Regnorum Britanniae Tractatus Vol. 60. Printed at the University Press by T. and A. Constable for the Scottish History Society, 1909.