In the full text of Honig v. Doe, the reasoning is:
As a condition of federal financial assistance, the Education of the Handicapped Act requires States to ensure a "free appropriate public education" for all disabled children within their jurisdictions. In aid of this goal, the Act establishes a comprehensive system of procedural safeguards designed to ensure parental participation in decisions concerning the education of their disabled children and to provide administrative and judicial review of any decisions with which those parents disagree. Among these safeguards is the so-called "stay-put" provision, which directs that a disabled child "shall remain in [his or her] then current educational placement" pending completion of any review proceedings, unless the parents and state or local educational agencies otherwise agree. 20 U.S.C. 1415(e)(3).It's not an issue of the Constitution -- Congress has enacted federal law which places certain conditions on schools which accept federal aid.
To cut the strings, schools must decline the federal funds. Some schools are deciding that this is the way to go. Utah, for example is considering a bill to opt out of "No Child Left Behind", and forego the federal funding. There comes a point where the damage and expense caused by federal regs can be seen to exceed the value of the federal funding.
And since it's legislation, all congress has to do is repeal it, and the courts have nothing further to say about it.
If you'll dig a little deeper, you'll see it wasn't all legislation. From your full text link:
Although these educational failings resulted in part from funding constraints, Congress recognized that the problem reflected more than a lack of financial resources at the state and local levels. Two federal-court decisions, which the Senate Report characterized as "landmark," see id., at 6, demonstrated that many disabled children were excluded pursuant to state statutes or local rules and policies, typically without any consultation with, or even notice to, their parents. See Mills v. Board of Education of District of Columbia, 348 F. Supp. 866 (DC 1972); Pennsylvania Assn. for Retarded Children v. Pennsylvania, 334 F. Supp. 1257 (ED Pa. 1971), and 343 F. Supp. 279 (1972) (PARC). Indeed, by the time of the EHA's enactment, parents had brought legal challenges to similar exclusionary practices in 27 other states. See S. Rep., at 6.
If you'll read Mills and PARC, you'll see that those decisions relied on the equal protection and due process clauses of the Constitution. Both Reinquist and Congress thought those two cases were very important. Even if the statute is repealed, the equal protection and due process clauses will remain, and I'd predict a slew of new court cases on those bases.
Actually though, I didn't think you'd be interested in Honig so much for the rationale, but because you'd mentioned the problem of behavior-disordered students disrupting classes for the others.