The flower blooms from Echeverias do take some nutrients from the plant, however they won’t cause it to grow leggy. Blooming is a normal part of the growing cycle for Echeverias.
Some succulents only bloom once in their lifetime though, and in this case, a bloom means the mother plant is finished growing and will die after blooming. Succulents that do this are called monocarpic. A few examples of monocarpic succulents include most Agaves, Sempervivums (hens and chicks), and Aeoniums.
With monocarpic varieties, they generally put off a lot of new baby plants before blooming, so you’re not really losing out on anything. Every once in a while you may purchase a new succulent that is monocarpic and it will bloom within the year. While not typical, this is possible.
The lifespan of a monocarpic succulent really varies. They can live anywhere from a couple years to several decades. No one is quite sure why some bloom more quickly than others.
For non-monocarpic species (like the Echeveria you mentioned) you can leave the bloom on until it dries out, or simply cut it off whenever you don’t like the look of it. The succulent will continue to grow as normal.