My answer to your question is the same as the one that "Punch" magazine once gave to gentlemen contemplating matrimony, DON'T
As an ex-married man, I can gel with that
As a photographer who had to start off with continuous lighting (because that's all that there was back then), the same view applies
As a photographer who has both shot video and shot stills during the videos, I understand both the pros and cons of both flash and continuous lighting.
Yes, there is one visual advantage with continuous lighting - it's brighter than a modelling lamp and so gives a much better idea of where the light and the shadows fall. No flash modelling lamp is bright enough to provide full information about lighting effects, and particularly not about shadow depth, unless the room is in total darkness, it's just a useful indication. Experienced photographers know this and do one of the following:
1. Exclude all light
2. Turn off room lighting and reduce the light as far as possible
3. Use their experience to visualise the result
4. Take a digital test shot and get the information from that.
Now look at the disadvantages.
1. Blindingly bright for the poor sitter - flash is on for such a tiny fraction of a second that many people don't even notice it.
2. Despite its dazzling nature, very low actual power, this requires a higher ISO setting and much longer shutter speeds, with the real possibility of both camera shake and subject movement.
3. The long shutter speeds introduce pollution from other light sources, removing precision from the lighting. Look at some of the lighting challenges in this forum - the people who have used continuous lighting cannot produce "pure"results because of light pollution.
4. Less accurate colour rendition. The CRI (Colour Rendition Index) of both daylight and flash is perfect, at 100. LED (and most other specific photographic continuous lights have a much lower CRI, and so cannot reproduce all colours accurately. The situation has improved a lot recently, and most manufacturers/sellers now claim a high CRI figure, but by no means all of them tell the truth, and it's beyond most of us to actually test their claims.
5. The better LED continuous lights are modelled on flash heads and have S-fit bayonet fittings that allow them to accept the essential light modifiers, but other designs don't, which makes them pretty useless for any type of creative lighting.
So, why are continuous lights so popular? Profit. They pretty much all have the same components, which cost very little. The genuine market for them is video, but they are marketed for still photography because the flash market is dominated by Godox and other manufacturers can't get a look in, so they've switched to continuous lighting, which pretty much anyone can make in a garden shed . . .