Spring attack can be countered simply by having the enemies ready actions to attack the barb when he comes within reach
I kinda knew that when I mentioned it:
They'd need to give up melee, and/or start triggering attacks on your approach rather than normal initiative.
However, it's metagamey for enemies to know to do this right away. Every single one, every single time, would need to experience this problem for him/her self and react to it, at which point a couple rounds of damage would have already been done.
and combat spiked chain by using foes with 10ft+ reach themselves
That's
really metagamey. A spiked chain build appears in your game world and suddenly the enemies are equipped with 10+ reach weapons? If a barbarian pours all his feats into his axe proficiency, do your enemies suddenly gain DR? If a player wants to play an Ignus build and torch the planet, is the game world suddenly populated by Efreeti?
Anything can be countered. That's not a good reason to say "don't bother with the build, try something else." The real question is,
how easy & frequently will it be countered?
Trip builds? Sometimes they win, sometimes they need other tactics. But it IS a viable build, unless you have a DM who isn't fighting fair. And someone moving at inhuman, and frankly, even faster-than-scary-monster speeds? That should surprise people. Lots of them. Frequently.
Consider that such characters would be moving at what -- to them -- felt like a normal walking speed but was actually a 3-minute mile. They would outpace our world's best runners, and they'd do it without breaking a sweat. If you let this build
run -- barbs get 5x speed -- that's 4500 feet in 1 minute. That's what, 55 miles per hour? This person would run onto a highway and keep up with traffic. To me, I either have to accept that the player has done something interesting and surprising -- and admit that they get some benefits from pouring feats and spells into it -- or else I have to declare the build taboo because it breaks the game even though it follows the rules.
The benefit is fairly minimal to a spellcaster, since there are few features worth giving up for access to higher lv spells.
With 4 levels of barbarian and what looks like a combat cleric, he hardly falls into the spellcaster arena. This isn't the kind of build where I'd say "you're losing spell levels!" It's more like a few dips into cleric domains to get some (surprising) buffs.