Two things you're missing --
1. TEC is basically a resistor, so at frequencies where we can ignore junk like lead inductance, yeah, it's a resistor. So, at 1.5kHz, that filter capacitor is probably going to have a low Q. Even lower still if you match sqrt(L/C) = resistance.
2. Even if you aren't varying it over any meaningful kind of time scale (i.e., 1.5kHz+), you still have startup transients. The inrush surge current is given by -- guess what, the same ratio, sqrt(L/C).
That is, if you have a step change from 0 to 10V (or 20V at 50% PWM, it's equivalent when F_PWM >> cutoff frequency), you'll get a peak current on the order of (10 - 0) / sqrt(L/C). So, for 33uH and 270uF, 28.6A (assuming the transistors deliver it at that point?).
I strongly recommend using a current mode control. Even just for running a dumb TEC, it's a good idea to use some kind of current limited switch. Preferably a fast enough one to do PWM + filter, and preferably the PWM control inside too, and cheap. Fortunately, these exist: just grab a switching regulator. Yes indeed, put in a full and proper regulated supply just to run a TEC. Why not?
(If you're scratching your head about control, just run a resistor from the control voltage input, to the feedback node. The CV looks like extra output voltage, so more CV = less Vout -- it's an inverting amplifier, with gain set by the ratio of resistors. If your source is ultimately PWM, an RCR filter will do.)
Tim