Mostly agree with Raszaron's sentiments above.
But I have another idea. Since BRZ is probably going to preclude an Impreza or WRX/STI AWD coupe... I have an alternative that won't step on BRZ's toes.
A Forester-based successor to the Brat, but updated.
Take Forester chassis... lengthen front doors, and eliminate rear doors, and the roof aft of the front seats. Rake the B-pillar forward similarly to the Brat, with a lower roof height than Forester over the front seats. Cargo won't be contained under a roof, so might as well lower the roof to reduce frontal area, and make the vehicle look sportier, longer, and lower, visually. Make the two side doors more like coupe length, for some inside stowage behind the front seats, without going to a full "extended cab".
Make the aft section of the body as a cargo bed, with re-enforced chassis rails underneath. Composite bed lining is fine to avoid rust, and weight, as long as it is robust. Bed side compartments somewhat like RamBox is fine, too. Heck, put composite aft-facing seats back there, to get around the chicken tax again, like the Baja had to. Make them unbolt easily, or detach from lugs in the floor, like minivan seats.
Give it a compound tail gate, like the Ridgeline, and a mid-gate/Switchback inner bed bulkhead like Baja, into the interior. Make it possible to mount a full-size spare tire under the bed liner as Forester does and Honda Ridgeline does, or along the inside of the bed rail, or to the exterior of the tailgate, owner's choice, depending on cargo configuration. People criticize Ridgeline for only having the spare tire under the bed liner, which necessitates unloading cargo to gain access, if there is cargo in the bed. Versatility in mounting the spare or multiple spares helps that.
In addition to the hard-roof version with the switchback bulkhead... I suggest another alternative... a roll-back soft-top. Basically similar, but with a collapsing, or fully removable cloth/vinyl top from the windshield header, cov over a brace between the tops of the B-pillar as rigidity and roll-over protection. Rolling back or removing the top panel, lowering the rear and side windows would open up four sides of the interior. Jeep wrangler seems to do well as a soft-top.
Use the FA25 engine with Legacy GT's 6MT as the base drivetrain. Auto or CVT option... whatever.
Engine package 1: EJ25 Turbo, or replacement FA/FB turbo option when it's ready. Backed by WRX STI 6MT, with locking DCCD feature for on & off road use, front and rear torsen LSDs. Applied to both 6MT and robust-upgraded 5EAT option as well.
Engine Package 2: Same drivetrain, except with a re-tuned version of the EZ36 6-cylinder boxer as the power source.
Engine Package 3: Boxer Turbo Diesel drivetrain from Forester in other markets.
5x114.3 hubs and bearings, with Tribeca-spec brakes and re-optimized Forester suspension as standard. Could be applied to whole Forester line.
Suspension upgrade package: STI Brembo brakes and bilstein inverted long-travel dampers with variable damping rate as optional upgrades. Normal, sport (stiffer), and off-road (relaxed damping rate) settings. Maybe with un-locking sway bars in the off-road mode.
Small airbags as variable ride height helper springs would be great, but maybe a bit much for most people. Similar in theory to some sports cars that have lifters to raise them above driveway approaches or speed bumps, but instead used to lift from a moderate ride height starting point. Starting point could be slightly lower than stock forester, but slightly higher than WRX STI, with fully collapsed airbags. Partially inflated airbags would gain most of the additional ground clearance, and reduce the effective spring rate for off-road... fully inflated would give maximum ride height, and re-firm the spring rate. Good diffs throughout, variable damping rates, dis-engaging anti-roll bars, and variable ride height would probably make it one of the best cross-terrain performance vehicles on the market, to be calibrated for firm on-road performance and stability, or configured for good suspension articulation for off-road. Not a rock crawler, but better than most CUVs off road... and much sportier on pavement than the likes of stiff-legged solid axle Jeep Wrangler.
It is a completely different prospect than a sport coupe, but with all the sporting equipment selected on the turbo + 6MT + Brembo/Bilstein variant, and a hard shell bed cover, it would still pass as a 2-door STI, that could scream on the tarmac, and then go off the pavement, too.
Plus, it could haul a little something if needed, and with re-enforced chassis rails under the bed, a towing receiver could allow some towing capability, probably at least as much as Tribeca is capable of, with plenty of power, big brakes, and robust hubs and bearings, and strong enough aft chassis structure. Baja couldn't tow on a trailer what it's small bed wouldn't handle. A small bed is fine, if a utility trailer is a possible alternative.