What the heck are you talking about? There is no such thing as an "illegal" secession, because there's no such thing as a "legal" one, either. Secession is the act of leaving an organization. Whether or not you follow the "rules" of the organization you just left is only relevant if you lose.
As for West Virginia... it seceded even more "illegally" than the Confederate states did (based on your standard). The Confederate states at least used the existing state governments to declare their separation. West Virginia was created because a second, unionist-backed Virginia government was formed in Wheeling that then voted to secede (over the objections of the established Virginia government in Richmond) and was recognized by the US Government. If there had not been a war, West Virginia would have been enjoined from statehood based on Article 4 Section 3 of the Constitution itself:
New States may be admitted by the Congress into this Union; but no new States shall be formed or erected within the Jurisdiction of any other State; nor any State be formed by the Junction of two or more States, or parts of States, without the Consent of the Legislatures of the States concerned as well as of the Congress.
Far from supporting the idea of a "legal" secession, the case of West Virginia shows that there is no such thing. The only legal secession is the one that succeeds, and the only "illegal" one is the one that fails.
But there was a war. Under the circumstances -- a state government gone into rebellion and taking up arms against the rest of the country -- West Virginia statehood wasn't much of a problem. When the state government was shooting at the rest of the country it was natural that an alternative "loyal" government would be set up, and West Virginia statehood got the approval of the state government that wasn't shooting at the constitutional federal government.
There was a question, though, of whether areas that didn't want to be included in the new state should have been part of it. And why is it worse when a state is broken up? If breaking up the union had been debated in congress or in a national convention, state borders might have been changed to accomodate areas like West Virginia or east Tennessee that weren't keen on secession.
The only legal secession is the one that succeeds, and the only "illegal" one is the one that fails.
This question of "legal" and "illegal" secession is a little beside the point. If there's a prescribed means of exiting some political union, we can talk of "legal" secession. If there isn't, an arranged separation by mutual consent would also be "legal."
In the absence of an authorized means of exit or separation, force may very well decide things. I don't think we should say that force should always be the arbiter of what's legal or constitutional and what isn't. That's why we probably want to avoid unilateral secession in favor of a settlement negotiated beforehand by the parties concerned.
Unfortunately, by the time secession or separation becomes a real possibility, people are so angry that they don't want to have negotiations or ask for consent. The act of declaring oneself independent on one's own comes to have great satsifaction for people.
Of course there could be a legal secession. There just hasn’t been one yet.
Nearly anything can be done by constitutional amendment:normally 2/3rds of each house of congress and 3/4s of the state legislatures.
It could perhaps even be done by simple legislation. 50% of each house plus one vote, and signature of each president.
It could also practically be accomplish by litigation, with the supreme court resolving a controversy between the state and the federal government as original jurisdiction.
Rebellion is an illegal process, but after a successful rebellion legality could be restored by a treaty: Signature of the President and 2/3rds of the Senate. Here is a question: Would a state bound on secession have its representative counted towards the 2/3rds in the Senate? Would a large plurality of the states able to pull off a successful rebellion, perhaps be so large that 2/3rds of the Senate was not possible without them so no treaty could be ratified?