What would happen if Protagoras v Euathlus were heard in court today? what would have happened if this case were to be tried in a modern-day courtroom?
Generally speaking, Protagoras's position would prevail under contract law.
Protagoras and Euathlus entered a contract in which the exchange of considerations involves tutoring and compensation therefor.
Since the agreement nowhere portrays compensation as contingent on Euathlus not declining to exercise as lawyer, the most reasonable inference is that the parties' understanding at the time of the formation of their contract implicitly ruled out that scenario.
Or at least that risk, which is under Euathlus's control, was not disclosed to Protagoras. Thus, the contingency cannot be said to be knowingly entered by Protagoras (contract law is premised, inter alia, on all the conditions being entered knowingly and willfully by the parties).
The paradox conveys that Euathlus changed his mind "after been trained". Even if ruling out Euahtlus's change of mind is viewed as a mistake of both parties which could make their contract voidable, Protagoras would entitled to restitution for the performance of his duties. See Restatement (Second) of Contracts at § 152(2).
The condition that compensation be made after Euathlus's first win in court can be interpreted twofold; namely, as:
Protagoras's acting as creditor towards Euathlus while the latter obtains funds with which to pay the tutoring; or
Protagoras's form of guarantee that the tutoring he provides to Euathlus is effective, since winning a case in court may be taken as evidence (again, if we assume that nowadays courts are "all integrity and honesty") of having received competent training.
Both interpretations strengthen Protagoras's legal position, as these evidence his commitment to the covenant of good faith and fair dealing, respectively. By contrast, Euathlus only benefited from both standpoints without giving anything in return to Protagoras.
Furthermore, Euathlus's eventual decision not to work as lawyer amounts to forfeiting the aforementioned guarantee, since his unilateral decision precludes testing the effectiveness of the tutoring he received.
Has thousands of years of legal development created a resolution to the paradox?
The Paradox of the Court is more of a philosophical challenge for beginners that stays there and leaves out many (im-)practicalities and legal issues. But an assumption that the Ancient Greeks would not have considered these aspects in a real-life controversy would be naive and oversimplistic, especially if we bear in mind the great intellectual development they achieved.
Here I only cited the Restatement (Second) of Contracts, which is frequently cited by U.S. courts deciding contract disputes. But I can assure you that many of these principles as well as issues of impracticalities were essentially (and perhaps similarly) addressed by Aristotle.