Yes...sort of. More at L1 than at other levels though.

For a brief look at this, let's look at the 4 basic L1 characters and see what their defined combat options are.

• Wizard: 3 L1 spells/day (they get the extra from an afternoon nap). 3-4 cantrips. Generally the wizard has the most combat options. They have more daily spells than the cleric and they have several offensive cantrips to choose from (firebolt and ray of frost are the two that come to mind, they have another). Their cantrips either do a good bit of damage or slow or push. This gives them good options in melee, at range and on the daily power front. Lots of options on their turn.

• Cleric: 2 L1 spells/day, 3-4 cantrips. The cleric only has 1 attack cantrip, but the current cleric is designed to be played by a dwarf, and they get a genuine melee option (with proper stat allocation, it's better than their cantrips at L1). This gives them a good number of options (several of their cantrips are cool utilities in combat too). So they have a good number of choices on their turn.

• Rogue: no spells, all powers phrased in the form of Melee Basic Attack, and their cool movement power doesn't kick in until L2. The L1 rogue's only way to reliably generate Sneak Attack is to actually get into melee and find a buddy to stand next to their target (The other way is to stay at range, and also find a buddy to stand next to their target). Otherwise the L1 rogue does spend half their turns hiding (which is sad). So yeah, limited options here in combat (L1 rogue out of combat is a skill monkey and that's cool). Most of the combat decision for the rogue are whether or not to eat an opportunity attack to go over to the fighter's target to deal Sneak Attack on it.

• Fighter: Even more boring than the rogue. He has two main choices: which target am I going to hit with my weapon, and is it time to burn my Second Wind. Granted, this makes the fighter the most self sufficient character, but it doesn't provide many interesting combat options. Similar to the rogue, the fighter's best option sometimes is to eat the Opportunity Attack and walk over to the rogue's target so he doesn't have to eat the OA himself.

So yeah, L1 is pretty boring for the Fighter and the Rogue. Here's the good news: L1 is designed to be very short. And L2 is where a ton of the good stuff is for the Fighter and the Rogue*. The Rogue gets their class defining power: Cunning Action. This lets them hide, move and attack all in one turn (or disengage, move and attack all in one). This is the power that makes the rogue tick in a lot of ways. For the Fighter, they get the power that lets them compete with the rogue in damage 1-20. Their Action Surge power gives them a second meaningful per rest choice in encounters: they get another action on their turn.

Neither of these choices really solves the "I attack the goblin with my sword until he's dead." However, in many ways, this isn't all that different from the level of choice an Essentials class character has on their turn in 4e (well, it's fewer options, but it's fairly close by L2 I think).

Ultimately, breaking the "I attack the goblin until he's dead" cycle is not something that 5e addresses very well. It's left to the players to "try something interesting" to get the upper hand, and this seems to be encouraged by the system. Like it or not, this is 5e's design paradigm for Basic D&D. With the PHB coming out next month, two new martial archetypes for the fighter, and two new sub classes for the rogue should provide them with additional options on their turn (Eldritch knight is a gish type with spells, and the Battle Master fighter uses combat expertise dice to do other stuff).

*I think there is a pretty good reason for this. I believe this is largely to limit the effectiveness of single level MC dips into fighter and rogue to get some of their strongest powers (they already get a lot at L1, the fighter alone gets a fighting style, weapon and armor profs, and Second Wind.).

There are 2 definitions of "round" in 5e. There is the definition of "round" that you quote, which is from initiative position intMax to initiative position 0 (or negative if you manage that some how).

Then there is the definition used here for readied actions. This is the same definition used in "once per round" effects such as certain powers. This definition begins at the beginning of your turn and ends at the beginning of your next turn.

Because (unlike in 4e), readying an action and activating it, doesn't move your initiative order position, and because it matches the readied action refresh timer (which happens to use the same 1/round definition of round), readied actions can be used at any point in either the current round or the next round prior to your turn.

Here's how reactions refresh:

When you take a reaction, you can’t take another one until the start of your next turn. If the reaction interrupts another creature’s turn, that creature can continue its turn right after the reaction. (Player's Basic p70)

This is a large part of the support that leads me (and many others) to believe that readied actions can roll up to your next turn.