Yes, the Wyvern is probably intended to have disadvantage.
While Word of God could always overturn this (but it didn't), it seems pretty clear that the intent is for this to apply to reach attacks. They have the key phrase "ranged attack" and use it elsewhere in the rules (e.g. in the Monk's deflect arrows ability). This heavily implies that the more awkward wording is there for a reason.
They might have worded it this way so that ranged attacks made from melee are normal, rather than disadvantaged. But I suspect this case is less likely than the reach attack one (your mileage may vary).
In other words, it's not a case where it looks like they used simple language and forgot about some corner cases, like the interaction between druids and lethal damage.
As to why this would be the case, consider that a large wyvern doesn't have a 10' body with a long head that sits 10' away. The entire wyvern occupies a 10'x10' space, and stretches or pounces when it needs to attack outside of reach. This kind of stretching / pouncing will inherently limit the creature's attack vectors, perhaps in a way that dropping to the ground will help.
In other words, the monster isn't right there. The monster is still 10' away.
Also remember that the monster doesn't have to stay at range. As soon as they drop prone, it can close to within 5' and start taking advantage on its attacks.
From a mechanical standpoint, this makes prone a general strategy to take for things attacking you that you can't reach and/or luring things into melee. This simplifies the mechanical design, and helps avoid loopholes.
As a house rule, you can certainly scale down the effectiveness of the prone condition. It's unlikely to break much with the current corpus of monsters. However, doing so will always compete with simply closing to melee and gaining advantage... And it is unlikely that this will be brought into the official rules (although maybe it will! Sloppy templating, etc.).
There are two different things happening here: your movement speed being halved, and spending half your movement speed. These work differently, and the order matters. The end result is that the grappler can't move-drag after standing up from prone. Here's how it works:
You start with your full movement speed.
Let's use 60′ for the sake of example.
Standing up costs half your movement.
Your current speed is 60′, half of which is 30′. To stand up you spend 30′ of movement. Your speed is still 60′.
Dragging while grappling halves your movement speed. Your movement speed this round has now been reduced to exactly how much you've already spent, so you will have 0 feet of movement to spend.
Your current speed is 60′, but attempting to move-drag a grappled opponent changes it to 30′. You have already spent 30′ of movement and have zero feet left to spend.
The end result is that after standing up, you still have half your movement left, but as soon as you try to drag a grappled opponent you will have no movement left and remain where you are, so realistically you won't bother trying to drag that round. (You could still end the grapple and move your remaining half movement though, of course.)
Best Answer
You are describing a sound tactic
(in the game and in the real world)
It has been said that the goal of military action is to take a fair fight, and make it unfair. Most of martial history, from drone strikes to throwing rocks from a high place, has been about giving yourself an advantage. And this is no different.
In the real world, when firing from behind cover, people often drop behind it completely to reload, or between shots. They see no need to expose their body to attack at all times, and instead choose to only become vulnerable when they intend to fire. You can think of this as similar to what your Rogue is doing: they expose themselves to danger when they need to, and otherwise stay prone.
And to claims that this is "cheese," keep in mind that this is tactically similar to using a Rogue's Cunning Action to Hide each round, and can be countered by most things that counter that (Medix2 gives some great examples , like having enemies Ready an action to attack the Rogue when exposed, or doing something that gives Disadvantage to the Rogue's attacks to rob them of Sneak Attack damage). Also, this tactic is not entirely without cost, because going prone every round has some inherent drawbacks.
What you give up doing this
There are two major things you lose with this tactic
1.) You are vulnerable to melee attacks while prone.
If you can get on the roof, then odds are good someone else can too. And as you stated, while a creature is prone (PHB, p. 292):
The higher up or less accessible the roof you're on, the less this is an issue. But you never know when an enemy might summon an ally, or unexpectedly cast the Fly spell, or quietly climb the wall. If you find yourself in melee range while prone, enemies will get advantage on their attacks.
Besides the mechanical vulnerability, you are also likely cut off from your allies. If your rooftop is hard to access, keep in mind that your close-range friends may have trouble coming to your aide. And you'd have some trouble reaching them as well, which brings me to my next point.
2.) You lose some mobility
Your strategy ensures that you lose half your standard movement every turn standing up. This could cause a problem if you need to move far in one round. Combat is dynamic: an enemy may move around the battlefield, perhaps moving out of your range, or into a place that has total cover from your vantage point. If this happens, you may not be able to keep up with them. Your cunning-action Dash makes this less of a problem, but you'll not only have to spend movement to stand up, but also to get down from the top of the roof.
Essentially, the more inaccessible you are, the safer you become, but the harder it is for you to adapt to enemy tactics. That being said, there are a lot of situations where going prone defensively then standing offensively is a great tactic! If you think it will help in your situation, I say "go for it."