When we're investing, we should be looking at our investment alternatives. I agree that the mortgage value and payment would both diminish in value fairly quickly at 15% inflation. But in this case, if we received historical stock returns (let's use 10% for easy calculations), the purchasing power of that equity would be diminishing even faster.
Another way to look at it, we're paying $30,000 per year in interest at the beginning of the mortgage (15%). If we had the $200,000 to pay it off immediately, we could either get an immediate return of $30,000 per year on those funds, or we could invest it in equities and expect to earn $20,000 in the first year. In the second year, we'd have that $30,000 per year (plus principal payments) invested into the stock market earning 3,000 per year plus the $30k from interest savings (for $33k total), whereas the alternative all equities investment would earn $22k. I imagine you can see where this is going. Here's the table showing that if you immediately paid off the mortgage, you'll eventually end up $1.75M richer than investing instead (granted, $1.75M would be equivalent to $20,000 if 15% inflation were to continue uninterrupted for 30 years).
POTM DPOYM
$- $200,000.00
$2,528.89 $201,666.67
$5,078.85 $203,347.22
$7,650.07 $205,041.78
$10,242.71 $206,750.46
$12,856.95 $208,473.38
$15,492.99 $210,210.66
$18,150.98 $211,962.42
$20,831.13 $213,728.77
$23,533.61 $215,509.84
$26,258.62 $217,305.76
$29,006.33 $219,116.64
(......................................)
$5,617,432.48 $3,902,172.68
$5,666,773.31 $3,934,690.78
$5,716,525.31 $3,967,479.87
At this point, the home is paid off and you're clearly ahead by paying off the mortgage. In this scenario, you would break even in your equities account in about 11 years (of course you're ahead on day two due to the equity in your home).
All of this is to show that inflation doesn't matter when investing in two different assets with little correlation to inflation. Since inflation affects both equally, it should essentially drop out of the equation and you should consider risks and expected returns in deciding where to invest.
ETA: Here's the full annual table:
Year POTM DPOYM
0 $- $200,000.00
1 $31,776.94 $220,942.61
2 $66,881.34 $244,078.19
3 $105,661.63 $269,636.37
4 $148,502.72 $297,870.82
5 $195,829.84 $329,061.79
6 $248,112.72 $363,518.86
7 $305,870.30 $401,584.03
8 $369,675.86 $443,635.13
9 $440,162.69 $490,089.52
10 $518,030.42 $541,408.30
11 $604,051.91 $598,100.82
12 $699,080.98 $660,729.79
13 $804,060.83 $729,916.84
14 $920,033.45 $806,348.67
15 $1,048,149.91 $890,783.91
16 $1,189,681.85 $984,060.63
17 $1,346,034.02 $1,087,104.63
18 $1,518,758.31 $1,200,938.69
19 $1,709,569.09 $1,326,692.67
20 $1,920,360.26 $1,465,614.73
21 $2,153,224.01 $1,619,083.74
22 $2,410,471.64 $1,788,622.97
23 $2,694,656.46 $1,975,915.16
24 $3,008,599.14 $2,182,819.30
25 $3,355,415.72 $2,411,389.00
26 $3,738,548.54 $2,663,892.94
27 $4,161,800.36 $2,942,837.35
28 $4,629,372.18 $3,250,990.87
29 $5,145,904.88 $3,591,412.10
30 $5,716,525.31 $3,967,479.87