Hmm, I never expected to solve this problem with a single element like this. Very good.
If there is a solid-state relay, why people keep using old mechanical relays? Are they cheaper?
Also - larger SSRs (not like the posted image) controlling larger currents require heatsinks, which adds to the cost. Something to check out is the various documents, faqs, etc at Omron's site:
Also AC SSR's do not break the circuit completely. There can be a very small amount of leakage current when they are off. In most line voltage applications this is irrelevant, but in some applications it can be important.