Mostly; what Crothian & Umbran said. I do have a point or two to add:
1) I've been told adventure writing is an art, but if you are simply following the direction of PCs does it require even more skill to pull off?
As Umbran said, "Different skills." Not more or less. However, one thing no one
* mentioned above is
player skill. Running in sandbox mode means the players have to raise their game and decide on a course of action (not wait for you to provide one). They need to show initiative and communicate what they want to do to the DM. That requires using some mental muscles on their parts that pre-written adventures don't really develop.
Running in sandbox mode is harder for players. Ultimately I believe it's more fun and more rewarding (that's been my experience, FWIW), but you can't just drop this mode of playing on them without warning. Also, it can be tough sometimes for new players or players who have only experienced pre-written adventures. They have to learn how to play this game too.
My take away is that DMs cannot switch from pre-written to sandbox without the players being fully engaged and on-board. Make sure they understand the benefits of this kind of play and also what is expected of them. More games have collapsed for lack of communication and un-met (unrealistic) expectations than out of any legitimate "bad experiences."
2) Does it dramatically increase the preparation time needed? (You may take this question however you feel.)
I think one of the best tools you can have is a series of random generators. Not just encounters, but cities, NPCs, thieves guilds, churches, cults, etc. Have lists of names handy organized by culture/race. That sort of thing. There are lots of resources already out there, plus you can make your own. Collecting all the generators and organizing them so you can find them in-game is some work, but once set up using them is easy. They embody the potential for a lifetime of gaming. It's an up-front cost that pays long dividends.
3) Would you recommend it to new DMs? And why or why not?
No. There are several skills needed for DM-ing. Running your sessions in "sandbox mode" is definitely the "no training wheels" version of being a DM. I think it's better and leads to much deeper PC immersion and fun (IMO), but it's definitely a system where you (the DM) are doing a lot of work adventure writers normally do for you (and often, you're doing it in real time while players are watching you). Once you can run a pre-written adventure well you can "graduate" to running sandbox.
*I didn't see Lord Pendragon's post until after I wrote this.