What's wrong with you people? Do you even know the purpose of braces on our cars?!?
the Celica is a UNIBODY car, in other words, there is no actual frame, the entire car is made from bent and formed sheet metal, that means, anywhere there is a stretch of sheet metal without any pre-formed framerails, there is going to be flex, and a lot of it for that matter. even the framerails will flex more than a car on a conventional steel frame. this is nice if you want a car with a cushy ride, but if you want precise and predictible handling, good traction, or safety in a crash, you need to tighen up a unibody chassis beyond stock tolerances.
Even if a bar is not connected to the strut towers, it makes little difference, you could weld bars to the strut towers, connecting them together and making them as stiff as possible, but if the rest of the connected chassis still flexes, you may as well be installing a strut bar on a pogo stick, since the chassis will still be flexing, and the suspension will still bob and flex in the end. The goal is to make that all-sheetmetal chassis more rigid; To get that go-kart feel, you need to stiffen up the entire car, and there are lots of methods to do this.
the purpose of an x-brace is to stiffen up the chassis in the cargo area. this is the biggest area of chassis flex on the whole car; it's wide open, sure, that hump in the back (that the bin usually covers) helps stiffen things up, but since it's a hatchback, you end up with a large, open pocket of sheetmetal that twists and bends more than you realize. add to that the spare tire well, which is usually formed from Fiberglass, and you have even more chassis flex.
Yes, a TRD
rear strut bar will help stiffen things up, it will limit vertical (left to right)flexing of the strut towers, but on a horizontal plane (front to back), they will still be flexing a lot, that's what the x-brace is there for, it stiffens up the rear chassis on a horizontal plane. this is why the better rear braces will have one or two more connection points that attacth to the floor of the trunk. the TRD
does not have this, they connect to the crossmember rail in the cargo area, but not to the cargo pan.
If you don't want to deal with all the braces and bars, a sure fire way to stiffen the chassis is to do what the honda guys do: pull up all the carpeting, remove the spray-on sound deadening insulation, and stitch-weld all the seams in the sheetmetal, this will make the chassis a lot stiffer than stock.
the best way by far is to weld in an actual 4 or 6-point cage.