High crossing isn’t inherently bad, it is just a terrible opener. The idea that high crossing causes you to leave lanes open is accurate, but it is incomplete. If you open with a high cross, you are definitely leaving a lane open; you’ve done nothing to close that lane and will probably get killed if your opponent is competent. You could double cross and bring your opposite side gear over to block the lanes your first cross left open, but that is usually just ugly. There are certain circumstances where this works, especially if you’re using a punch instead of a strap shield, but as a general concept it is a terrible idea.
However, physically blocking a lane with your equipment is not the only way to protect a lane. You can also protect a lane by causing your opponent to choose not to exploit it. The most common example of this is feinting an attack to cause your opponent to form a block. Since your opponent is blocking, your “open” lane is now as well protected as it would be if you left your sword in position to block.
You can also protect a lane by physically rendering your opponent unable to attack the lane. This typically means that your opponent is off-footed or otherwise unable to physically perform the appropriate strike. One way you can cause this condition to come about is by body fakes, but it also often happens organically as part of the evolution of an engagement. Spotting when your opponent has entered this state gives you the opportunity to throw otherwise risky shots like the high cross safely. Put another way, you can opportunistically throw the high cross when your opponent screws up in a way that makes them unable to retaliate to your open lane.
Alternately, you can block a lane with your opponent’s equipment. The most common form of this is to get them to block their weapon motion by getting them to use their shield to block their sword side by feinting a sword-side attack.
You can defend a lane by physically blocking it with your equipment, causing your opponent to be unwilling to throw into the lane either by feinting or by making them think it is an uninviting bait, causing your opponent to be physically unable to attack the lane, or by clogging the lane with your opponent’s gear. All of these conditions can be achieved during the course of an engagement, but none of them are present at the beginning of an engagement. Thus, the high cross, which inherently leaves a lane open, is not suited for use as an opener at the beginning of combat, but can be used successfully as combat evolves.