There is a warr currently in Discord about this issue, it's a mess as usual when a lot of people are participating at the same time, so this would be a nice place to copy some of the more coherent arguments.
(a) people who can only log on once per turn are screwed either way (unitwaittime or not)
(b) Freeciv is a turn-based game, not an RTS game
(c) double-turning throws the rest of the game's balance out the window, because it allows performing an attack from a safe place with next to no way to stop it. It makes killstack and the fact that AttackStrong units have low defense redundant, since defense outside of fortified positions will never happen
(d) the only real problem currently mentioned is that coordinating allied operations (around the turn change) is more difficult
Also a thought experiment I did:
Let's divide players into three groups: Firstly, the people who log on once a day for an hour or so. Secondly, the players who log on once in the morning for maybe 15 minutes, once at noon for maybe 30 and once in the evening for maybe 3 hours. Thirdly, the players who are able and willing to be online at any time.
Now, let's see what happens without unitwaittime: The first group – let's call them "casual players" – can always make their moves. They don't get any special advantages or disadvatages, except when they get to late-game when their units and cities don't fit into their hour anymore. The second group – let's call them "moderate players" – can do their turns normally. They don't get any special advantages or disadvantages, as they should generally be able to properly do their turn throughout the different parts of the day. The third group, however – let's call them "powergamers" – will focus all their actions on the turn change. They will be able to perform double moves and react in real-time, gaining a huge advantage over the first two groups. Additionally, when double-turning, the current balance of most units doesn't work that well anymore. Both casual and moderate players will be overwhelmed by their attacks, unless their time window just happens to be around the turn change.
So, what would happen with a 1 hour unitwaittime? Well, the casual players would occasionally lose their turn. The moderate players wouldn't be affected much, as their activity is spread throughout the day. The powergamers would encounter difficulties when double-turning against other powergamers (or players who happen to be online right now), since the other side can always react as long as they're online. However, most of the time, they will still have an edge against the causal and moderate players, since they will be offline for more than an hour, so if the turn change falls into their offline period, they can't react.
Next up: 6 hours unitwaittime. No difference for the casuals as compared to 1 hour; they'd still lose one in 24 turns. Not much of an issue for the moderates, as they still have their move spread over the day. However, the powergamers will now have a harder time double-turning against moderates, since the unitwaittime might include both their morning and noon logins, allowing them to react to anything around a turn change inbetween. Double moves would be less common, the powergamers' advantage would be slightly diminished.
And with 10 hours, it still wouldn't get any worse for the casuals, wouldn't really get any worse for the moderates – they might sometimes have to wait, but it shouldn't be a problem since they have enough time – but the powergamers would lose their edge. Even if the turn change is at night, they wouldn't be able to effectively double-turn, since the end of a moderate's evening activity and theeir morning login are close enough to one another that only one move can be done inbetween. Thus, the problem of double moves is solved (except against casuals), and really, the only one directly suffering are the casuals, who probably (a) didn't stand too much of a chance anyways and (b) don't take their losses that seriously anyways.
In summary: A short unitwaittime isn't really better than no unitwaittime. A long unitwaittime makes it so that moderate players (who have a life other than the game) stand a chance against powergamers – which is a good thing IMO, because we should be encouraging people to do things other than the game – working, studying, going outside, and most importantly: getting a full night's rest.
A turn lasts 23 hours. You are prohibited from moving a particular unit in the FIRST 10 hours of that turn IF and ONLY IF you moved that unit in the last seconds of the previous turn. If you moved that unit earlier, then you have to wait less or none at all.
If you want to move that unit at the start of the turn, then PLAN AHEAD or MAKE A RESERVE, and DON'T MOVE THAT UNIT IN THE LAST 10 HOURS OF THE PREVIOUS TURN.