This is a subject that I have always found fascinating, but that I've never actually tried myself. So fair waning - I may not know what I'm talking about!
The problem with cutting a curved pen stand like this from a single board is that the finished stand is fairly thin, which means that there are sections as you move away from the center of the arc where the fibers in the wood are rather short - which means that there will be weak points that can break if too much pressure is applied on the curve. So the question is how to avoid that problem.
Bending the wood means that the fibers will run from one end of the arc to the other, avoiding the short fiber problem. OP proposed steam bending using an ordinary steam iron as a source of humidity and heat. My intuitive thought is that a steam iron won't produce enough heat or steam for long enough to be able to bend the tight radius that he wants to achieve.
Another solution is a glued lamination comprised of three or more thin layers of wood. But the problem with applying the bent lamination technique for this project is that the desired arc has a fairly tight radius which requires rather extreme bending.
But what about combining the notion of steaming with the lamination technique. Obviously, you can't glue wet wood, so it would seem that these two techniques are conflicting. However, I found this video ( ihttps://www.youtube.com/watch?v=g7FuNHshRnw) in which the maker demonstrates a two-step proces in which he first bends the individual laminations, allows them to dry while bent, and then glue them together, with both the bending and gluing taking place in the same form. Also, rather than using some kind of specialty steaming jig, he simply soaks the thin laminations in water prior to bending. To me, that approach might be the simplest way to achieve a curved stand in which the wood fibers are continuous from one end of the arc to the other.
The other point that I noted in researching this question is that while PVA glue is normally the preferred adhesive for gluing wood, there is a problem when using it to glue laminations. Specifically, PVA requires air to cure, and if there are multiple laminations, it may take longer for air to get into the center of the glue-up to cure the PVA. That's not an obstacle, but it does mean that the glue-up must remain in the clamps for much longer to assure that the glue has fully cured - potentially several days depending on how many laminations are involved. An alternative is to use a good-quality epoxy that cures chemically rather than from air contact.
