I can cut off a sprig of many types of plants and put it in water, and it will send out roots. I have a bunch of spearmint that I did this with. Why don’t cut flowers sprout roots when I put them in water?
Most of the species used for cut flowers can’t be rooted in water (or put another way, most of the plants that will root in water are not species used for cut flowers).
However, you can sometimes take cuttings from cut flower stems, if they have the right parts (which may be nodes or semi-ripe tissue). As long as the flowers are present, the plant will typically prioritise its development, so if you have viable pieces for cuttings, you also need to remove the flowers.
To clarify a bit further:
A cut flower stem which has no vegetative component and/or nodes to yield future sprouts is typically (if not universally) a horticultural dead end. Branches with foliage and flowers will often root in water, though the flowers should be removed to concentrate development in new green growth (roses are an example of a common cut flower whose stems under the right circumstances can be rooted in water).
A disadvantage of rooting cuttings in water is that the roots are generally soft and succulent, and break more easily when eventually transferred to the ground outdoors or soil in a pot. Additionally, it’s a bit of a shock to the young plant to have to adjust to life in soil.
Some types of plants (i.e. cacti) are not going to be good candidates for rooting in water no matter what you do.
I have rooted cuttings from miniature roses and butterfly bushes. As noted, the flowers take energy away so it’s a good idea to lop them off.
Sometimes I’ll see roots growing on cut flowers regardless. But the stem and flower part is too large and there’s not going to be a viable plant. The plant will die and rot before any fresh growth can get started.
For best results cut a fresh end off, dip in rooting powder, put in water. A small, new growth piece is best.