Whenever I've had to use it in prod (in heavy OLTP environments) the seriousness of the issue has always outweighed any performance concerns. Ditto tcpdump. Often it was used specifically to determine the cause of performance issues. In any case you generally only strace 1 process, and if your application stack depends on one process you're probably in other kinds of trouble... unless it's erlang :)
It's not a choice between strace or nothing. It's a choice between strace, ftrace, perf, or eBPF -- and that's just the Linux builtins. Many low overhead addons can also do syscall tracing (sysdig, LTTng).
I often run ftrace, perf, and eBPF on our production instances for syscall tracing. If I ran strace, the instance would suddenly be very slow, and it would trigger Hysterix (and other) timeouts and be removed from the ASG and auto terminated. Our environment is fault-tolerant, so yes, we can run strace -- you just don't get much output, and the load vanishes from the instance you are looking at.
Last time I tried `perf trace` I realized how many things strace does that I take for granted. Things like file handle to filename resolution and pretty printing read() and write() buffers.
"perf trace" has improved since I wrote that, and may well be mostly strace-equivalent (but without crippling overhead) in the latest Linux.