I think my take that "provoking and emcouraging movement is an issue for 4e GMs" stems from the unfortunately pervasive "combat slog is inherent to 4e" meme.
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My sense is the issue (insofar that there is one) is multifaceted:
1) too many damn players at the table (which will feed back into too many enemy units if you aren't using hazards as a healthy part of your encounter budget)..
2) too many players not putting in the effort to minimize the handling time of their on-turn and off-turn actions.
3) GMs not framing combats around "extra-HP-ablation goals."
4) GMs not leveraging the inherent dynamism of the combat engine by failing to provoke or encourage movement (and stunting). Which is a head-scratcher because the system advocates it heavily and shows you how.
The first two are group/player issues. The latter two are GM-side. 4, by itself, goes a loooooooooooong way toward mitigating "sloggines."
We play with one GM and 5 players. And we are a bunch of lazy middle-aged guys, so we're not always moving at the speed of light! But (as I hope the actual play posts show) our combats don't just turn it "roll, hit, damage" until one side or the other is ablated. There's action going on and decisions being made.
4e encourages movement and gives you all the tools to facilitate dynamic (spatially, decision point-wise, and narratively) combat. It should become intuitive after a fair go (or immediately if you have prior exposure)
I have to be honest, it does intimidate a bit ^^ Luckily, i also heard that 4e is "easy" on the GM (on the internet but also from a friend of mine who DM'd 4e for a while)
The first adventure I used in my 4e game was the old B/X module Night's Dark Terror. I would recommend it to any 4e GM. (I had a physical copy, but it's
available on DriveThru for US$5.)
I had the PCs meet in a tavern (of course!). Then the first encounter was a fairly light-hearted social one, in which the patron NPC approaches them and recruits them for a mission. I remember the player of the wizard using his Mage Hand cantrip to tip his hat; and that the patron recognised the wizard's family name and compared notes on his uncle. From the more "meta" point of view, it didn't just give the PCs a misssion, but helped establish the feel of the setting and embed the PCs/players into the setting.
The first real encounter was with cultists blocking the PCs' boat on the river. Ranged attacks from the bank; an enemy mage using a raft as a firing platform; sandbars that the PCs tried to jump/teleport to; everything [MENTION=6696971]Manbearcat[/MENTION] and I have said about movement, space, tactical decisions etc was there in the first encounter. (I think the NPCs included a halfling slinger on the bank, a human guard and human mage on the raft, and 5 or so cultist minions swimming through the river to engage the PCs. There might have been a bandit somewhere there too.)
The mage and halfling surrendered, and the PC paladin took the mage into indenture. (Later on she was killed, and rose as a wight to get her revenge on the paladin. And then, later on again, a goblin shaman conjured her back as a wraith to get yet more vengeance on the paladin and other PCs.)
The next encounter was an abandoned home, with a bear there. The PCs, led by the paladin, befriended rather than beat up the bear, and so the paladin arrived at the homestead with two allies in tow.
The module comes with a big map of the homestead, and the centrepiece is a night-time goblin assault. I was able to use the different 1st and 2nd level goblins from the MM - so of the 20-odd goblins the module called for, probably half were minions and the rest a mix of standards and maybe one elite underboss.
Anyway, I've gone through the above to give a sense of how a GM can adapt an old module to good effect in a 4e game.