Double-edged Razors, are amazing & have some downsides. Some ideas.

TL;DR: Not everything about double-edged razors is solely an improvement, but I still do like them & recommend them to people!
I used them daily for years, hence I can rather confidently state the following will apply for many -but at all- people. Since people have different faces, contours, hand-eye coordination, skin, beard growth, amount of free time to shave in the morning etc, YMMV.
a. You will cut yourself.
I don't care how skilled you are, but in the first year of using your double edged razor you certainly will cut yourself a number of times and likely even after years of practice, it still happens once in a blue moon. These cuts are almost always more frequent and deeper than any you would get with the modern cartridge systems. This point relates to point b. below.
I have also cut my fingers pretty badly a few times trying to unscrew a stuck double edged razor head, a butterfly / trapdoor style sorts out this problem, though you may have to -rarely- chuck it in boiling water if it is ever really stuck.
b. You may get scarring if you are unlucky.
I ended up cutting myself around cheek bone area, unfortunately (and that was on me of course) I shaved a few days later in shower without mirror, cut the same area/scab, not small scar/skin stain. Years laters, it is slowly fading, but not sure it will ever go away completely. In all the years of shaving with cartridge systems before I never had that. They are just a bit safer/a little less likely to slice something off. Corner of the mouth also is a tricky area, with any design, but with double-edged razors even more so.
c. Slower, for reasons 1. and 2.
And, due to the design double-edged razors will always be slower than cartridge systems.
d. Traveling is less handy.
It is a 2 to 4 times bigger, heavier, and way more valuable item then modern disposable razors when traveling. Also, most airport security checks will not let you take a single double-edged blade if they notice it on their X-ray scans. It is at best a 50/50 shot that they miss it...
I experience a number of times that upon arrival in another country, I went a day or two or longer without shaving, while I sourced blades.
There is a solution for only the first issue: Wilkinson Sword, Gillette and others make very light, cheap and decent plastic double edged blade safety razors, good for travel.
But you will still be stuck without blades upon arrival, until you find some. Not great if you have a meeting soon after landing or happen to be in a country where double-edge blades are just not around that much.

I certainly recommend the plastic razor above to see if you like shaving this way, at around €5 to €7 for the razor, including 5 blades, it is worth having. Should you ever upgrade, the plastic one can still be a travel razor.
e. You will need water -and likely foam- to shave.
If you have little beard growth like me, shaving with solely warm water in the shower is totally possible with modern systems, not impossible with double edge, but certainly less safe, slower and harsher on the skin. This relates to c.
To use a DE properly, you need more practice, time and ideally of course a lather or foam, a mirror and patience. People with heavier beard always talk about how you need foam, hot water, two passes and lots of time. That is fine if you like that. If you enjoying spoiling yourself a bit and love the ritual of it, awesome! But I on the other hand,.. Nine out of ten times, I just want to shave and be done and go as soon as possible.
f. There may be faster and easier and totally cut-free alternatives.
Since I got an ancient used plug-in BRAUN sixtant type electric shaver, my double edge is mostly for 5 second touch-ups or rare use. The BRAUN lasts essentially forever (plug in, no battery), I need not have a mirror, nor any water nor foam involved nor pay any attention and can shave within literally 30 seconds. The safety razor, it is more like 3+ minutes to do it at all properly and safely and it involves mirror, attention, water and foam and rinsing.
This may not sound like a big deal, but it is to me! The electric is so much less hassle and time in the morning, before coffee, my work etc. Electric is a no-brainer to shave or trim, any time or any place. Safety razor not so. Sure, the BRAUN leaves a very slight stubble, it is not as close a shave as a double-edge, but certainly close enough. But I like the look and it feels good and my skin gets lot less abrasion and 0 worries about cuts, (warm) water, mirror, foam, cleaning up etc.
g. It might not be that cheap if you are not good at curbing spending.
Most people who get into Double Edged shaving end up not saving that much money or at least not the first 3 years, because it quickly becomes a hobby/collection: always looking for a better razor, trying new blades, nice foam, brush, rack or stand to hang it all etc. Not necessarily! But in practice, it happens a lot, just look around any forums.
Still: if I was going to advice someone new, i'd say: after the plastic one, if you are keen, buy a nice metal one, at once. = 60s adjustable Gillette in great condition or the closest modern stainless equivalent, 100 pack of most recommended basic but solid blades, simple but good brush, Proraso foam, done.
h. Your razor might be a bit dirtier.
In my case all double edge razors (and I have had about 6, very varied ones) trap a lot of beard hair, dead skin cells and other gunk during use, more and thicker crust of detritus than in modern systems I feel. Not a huge deal. But you do need to open and briefly clean them thoroughly with say an old toothbrush every time you replace the blade. For that reason, I really prefer the butterfly/trap door designs. I never got an issue or infection from using either style of razor.
So do I hate double-edged safety razors? Will I stop using them? **Not at all! I am still very happy I got into to them and will not go back to modern systems++, I find all the plastic and waste, environmental impact and ludicrous costs, marketing and rip-off or modern -plastic- systems offensive!
But, I will keep using my BRAUN electric mostly and safety razors only very occasionally, I have a few, mostly for touch ups or for rare days I want a very close shave. YMMV!
I am not trying to offend anyone or start a flame-war ("SKILL ISSUE!", "you have the wrong razor!" "lazy" etc) with this blog post. I am simply sharing my experience, in the hope that more people get into double-edge shaving yet also have a clear understanding of what it involves, possible (avoidable) pit-falls and what some downsides are.