Let's look at the chart and I've added a little waypoint I named "ASEDEAD" in Foreflight, as in... You're dead.
At 90 knots, you have two minutes before you run into an 11,000' ridgeline if you go-around at KASE. You have another 1:31 if you make a hard left to climb through 9000' to clear the lower ridge.
That's "ASETURN" the second waypoint charted.
The airport is at 7820' MSL. What's your Vy climb rate at max power in your POH for 8000'?
Now let's bump the standard temperature up and lets say Density Altitude at the surface is 10,000' MSL. What is your aircraft's climb rate at 10,000' MSL? 500 FPM? Lower?
It's coming up on midnight and 39F up there tonight as I type this. DA is 8305' MSL. It's not even summer yet.
Let's say it's always 29.92 for pressure up there just for this example... At the surface at 7820, it only needs to be 66F temperature-wise for a 10,022' MSL Density Altitude. Last time I was up there we were pushing the Colorado Pilot's Association recommended no-go limit of 75F. Almost 10,500' DA and we hadn't even taken off yet.
Check the performance charts in your POH to see what your expected takeoff ground roll is at 10,500' DA. (Hint: It's off the top of the chart in my Cessna 182P POH. You have to interpolate!)
Back to our hapless go-around guy ...
It is very unlikely you're climbing 500 FPM at 11,000' DA in my aircraft. (Remember DA of 10,500' at the surface, rises as you climb. At 500' AGL you're now looking at 11,000' DA for your performance numbers.)
Now what happens to your rate of climb in a turn? Ahhh... That's right. Two lift vectors. Some of that book number gets lost to this not being a straight-ahead wings-level climb out. Uh oh.
You definitely can't out-climb that terrain ahead. But can you cross the 9000' ridge, or will you have to continue the turn back toward and over the airport? Shallow circle? Claw your way to pattern altitude and head downhill toward Basalt?
This is just one scenario.
If the wind is high aloft out of the north, the back-side downdrafts off of that area marked "The Ridge" are going to be pretty intense. If you're climbing even 500 FPM and get a 200-300 FPM downdraft as you get close to the Ridge, now what? 1000 FPM downdrafts are not uncommon if the wind is high. All depends on where it crosses the ridges, at what angle, and at what speed.
This is the kind of stuff you think about when Mountain flying in Colorado. The airports are paved and you're not dealing so much with "back-country" flying as if you were up flying with the folks up around McCall, ID.
Instead, you're right at the edge of your aircraft's climb performance limits and always looking for "an out". An escape route. Usually downhill. Your turbo helps. A lot. You have more horsepower but the wings are still at 10,500'. Again, everyone's aircraft are different so meticulous study of the POH is in order.
By the way, your human body is also experiencing that DA. Did you bring the oxygen bottle? FAA rules are in altimeter numbers. Real world oxygen needs are in DA. Something to think about on a hot day in the mountains. If your engine won't perform as well at 10,000' DA, neither will your lungs.
Frankly... I love it. All of it.
But it carries higher risks than running around the pattern at a 3000' MSL airport.