Not only is LEA more flexible I believe it's preferred to SHL even for simple operations because it doesn't modify the flags register which can make it easier to schedule.
replyIt's more about the non-destructive destination part, which can avoid a move. Compilers tend to prefer SHL/SAL of LEA because its encoding is shorter: https://godbolt.org/z/9Tsq3hKnY
replyshlx doesn't alter the flag register.
replySHLX does not support an immediate operand. Non-destructive shifts with immediate operands only arrive with APX, where they are among the most commonly used instructions (besides paired pushes/pops).
replyUsing an lea is better when you want to put the result in a different register than the source and/or you don't want to modify the flags registers. shlx also avoids modifying flags, but you can't shift by an immediate, so you need to load the constant into a register beforehand. In terms of speed, all these options are basically equivalent, although with very slightly different costs to instruction caches and the register renaming in the scheduler. In terms of execution, a shift is always 1 cycle on modern hardware.
replyThey use LEA for multiplying with small constants up to 9 (not only with powers of two, but also with 3, 5 and 9; even more values could be achieved with two LEA, but it may not be worthwhile).
replyFor multiplying with powers of two greater or equal to 16, they use shift left, because LEA can no longer be used.