They seemed to do this on purpose, to add another layer of unpredictability. Beach clearly stated that they wanted every game to be different and thoughtful decisions to be made very turn as opposed to the standard (scout, scout, monument/shrine, settler of Civ 5). The only downside is that now I explore with two warriors together and ditch the scouts. One solution would be to give scouts an added combat bonus against barbarians.
I don't think it's done that. You have to open with military units. It's not like you have a strategic choice between a monument or a slinger.
A lot has been written on how to deal with Barbs. I would remember:
a) They are actually helping you, if you deal with them better than A.I.
b) They can help get the Archery Eureka. So I always start with a slinger
c) If you look at all the military units you need to get all the Eurekas/ Inspirations, it's a fair amount (3 ranged, an Anti-Cavalry, 3 melee, 3 heavy chariots - and that is just land, non-siege). You can build 3 slingers into 3 warriors, promote the slingers to Archers, get a spearman, three heavy chariots, and you won't be that far behind, even if planning a non-military victory. If you are on a coast you can get two galleys and a quadrieme as well. I'm not saying you'ld start like this without a lot of barbs, but it's generally more efficient to build first, promote later, than hard build, so again, you're not at such a disadvantage.
d) It's much easier to win even non-domination taking from cities from the A.I.
e) You can get level 1 promotion easily fighting the barbs.
f) they can't take your city (or kill the unit in their). So keep rotating/ healing units.
g) I don't know why, but the AI slams into you even if they lose. So unless you're facing a horse archer, put your 3 melees on good terrain inside your capital, set to fortify until healed, and watch every turn but you may get the promotion even before you have to rotate.
h) there are some very good youtube video out there. I don't have time to make them. Even if they are not against barbs, anything military based will help.
Can you post the original save?
I don't know why people disliked my idea of dropping down a level. An alternative is to use an A tier civ with an early unique. Sumeria might be a good choice (and the only time I don't start slinger).
I get it that people want to be able to play expand/ builder only - Civ V was great for that. I think it's reasonable to turn off barbs if you want that. But I think that would make higher levels more difficult, not less.
I also remember Civ3 had 5 gradients of Barbarians. I didn't like Civ3 and stopped playing after I beat Sid, but I didn't think all the options were a bad idea.