Code P0971 is set by the PCM when it detects that the pressure control solenoid "C" control circuit is experiencing a high voltage condition and therefore is not functioning properly.

Causes for this P0971 transmission code may include:
Defective pressure control solenoid
Contaminated transmission fluid
Restricted transmission filter
Defective transmission pump
Defective transmission valve body
Blocked hydraulic passages
Corroded or damaged connector
Faulty or damaged wiring
Faulty PCM

What specific diagnosis and repair is your mechanic recommending - based upon this list given of possible causes?
Hopefully, the mechanic is not suggesting that you replace your vehicle because of a corroded or damaged electrical connector on the pressure control solenoid?

The first step is to check the fluid level and examine the condition of the fluid for contamination. Prior to changing the fluid, you should (if possible) check the vehicle records to verify the last time that the filter and fluid was changed.
A detailed visual inspection to check the condition of the wiring for obvious defects is next. Check the connectors and connections for security, corrosion and damaged pins. This should include all wiring and connectors to the transmission pressure control solenoids, the transmission pump and the PCM.

Based on the specific configuration, the transmission pump may be driven electrically or mechanically.

List of Common Repairs: in order of expense / cost (estimated)

Cleaning corrosion from connectors = $10.00 (aerosol can of electrical contact cleaner)

Flash (reflash) PCM = $20.00 to $50.00

Repair or replace faulty wiring = $50.00 - $300.00

Flush transmission to clean passages = $50.00 - $100.00

Changing the fluid and filter = $40.00 - $100.00
Replacement filter = BECK/ARNLEY 0440405 {#31835AA030} - or it's equivalent

Replace defective Pressure Control Solenoid = $150.00 ~ $300.00
Repair or replace a faulty transmission pump
Repair or replace defective transmission valve body
Replace defective PCM

Before you consider any repairs, always obtain two or three written, detailed repair estimates for the same work - from reputable repair shops in your area.

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There have been multiple Technical Service Bulletins (TSB) issued for Subaru's CVT
Over the years, TSBs for the CVT transmission have popped up alerting dealerships and mechanics of these problems.

TSB 16-90-13R - This TSB covered the 2010-2012 Legacy and Outback following customers experienced sensations similar to "coming to a stop in a manual transmission and failing to depress the clutch."
TSB 16-103-16R - Covering all 2010-2015 models with TR690 CVTs, this TSB addressed leaking transmission fluid in the torque converter cases. The leaks were traced to failed gaskets in the CVT's oil pump chain covers.
TSB 16-102-16 - Talks about secondary oil pressure sensor diagnostics in all models.
TSB 16-104-17 - Covers the 2015 Legacy and Outback following complaints of "bumping" from the transmissions at idle. Owners described it like getting rear-ended.

Subaru's CVT Warranty Extension
In late November 2017, Subaru extended their CVT warranty for 1.5 million vehicles.

The automaker was quick to point out, however, this doesn't admit a safety defect. It's likely that a spike in out-of-warranty claims and online complaints helped drive this change, as well as the potential of future litigation if Subaru didn't act soon.

The extension bumps coverage for the CVT up to 10 years/100,000 mile. However, it does not apply to salvaged or rebuilt CVTs. And, in order to qualify owners must have their transmissions inspected or repaired before July 31, 2018.

Vehicles covered by the extended CVT warranty
2013-2015 XV Crosstrek (4th gen)
2014-2015 Crosstrek Hybrid (4th gen)
2012-2015 Impreza (4th gen)
2014-2015 Forester (4th gen)
2010-2015 Legacy (5th gen) and (6th gen)
2010-2015 Outback (5th gen) and (6th gen)
2015 WRX (4th gen)