FSWs have manouverability advantages at low-to-transonic speeds, but suffer at supersonic speeds due to the wingtips encroaching on, or penetrating, the shock wave. They also have very high stresses at the wing roots due to twisting forces, aeroelasticity problems from bending forces at the wingtips, lousy RCS beam profiles, and it is much more difficult to locate underwing stores, because you get very tail-heavy, very fast.
At high speeds and AOAs, when the wingtip starts to bend up, the problems compound rapidly. The air catches under the tip, increasing its angle of attack and therefore its lift. The other wing sees a similar increase in lift, causing the tips to develop a bit more wash in. This adds to the bending force on each wing, causing it to bend up and wash in even more. This causes a further increase in lift, which causes additional bending, which causes additional lift, etc, until the wing spars eventually have enough and you experience structural failure.
There are things that can be done to overcome some of these problems. The wing can be built extremely stiff with composite materials, and can be designed to wash out as it bends upwards, but the more sweep you use, the heavier the wing must be, and designing washout with different materials is very complex. For example, the X-29 used titanium forward spars (stiff), aluminum after spars (flexible), and carbon fiber skins with oriented grains that were designed to twist as they bent up.
FSWs look neat, but they are just not very practical. As has been mentioned, the SU-47 was a TD, like the X-29. It's not really known how effectively the Russians addressed the issues inherent to FSWs, but it would not be a cheap AC to build, even if the disadvantages were overcome.