If the Ready action allowed both movement and another action, it would totally break the action economy because it would allow this:
"I move 30 feet away from the orc, then I take the Ready action. When Bob says 'Now!', I'll fire an arrow at the orc, and move another 30 feet away from it."
Speaking is a free action that you can take when it's not your turn, so Bob will just say "Now!" as soon as I finish my normal movement. I've just effectively gained an extra 30 feet of movement at the lesser cost of consuming my reaction.
Here's another example of how this interpretation could be exploited:
"I move 30 feet across the field, then I take the Ready action. When Bob says 'Now!', I'll take the Dash action and move my speed, which will be 60 feet, across the field."
Again, Bob will say "Now!" while it's still my turn, so even if you were to argue that the Dash action doesn't increase your speed, only grants you extra movement, and thus doesn't increase the amount of movement you'd supposedly get from the Ready action's "move up to your speed"; even then, it's still your turn when Bob speaks, so you'd be able to just use Dash's bonus movement normally instead. Either way, you effectively got to move 3x your speed in one turn.
Because both of those scenarios lead to being able to do more in one turn than you could otherwise do, it's clear that Ready should not allow both movement and another action.
Now, with all that being said - as a DM, I've proposed the following house rule to my group, with the caveat that I may add one or more limitations, or fully rescind it, without notice, if at any time I feel that it doesn't play well:
If you don't use all of your movement on your turn, you can use whatever movement remains along with the action chosen from your Ready action.
Possible limitation #1: you cannot do this if you chose the "move up to your speed in response" option for Ready.
Possible limitation #2: it's all or nothing; you can only do this if you don't use any movement during your turn.
Possible limitation #3: when you use this option, for the remainder of the encounter, your initiative order changes to the position in which your reaction takes place (like 3.5's Delay action).
However, we have not yet tested this house rule. If and when we do, I can update this answer with the results.