(I have no acredited knowledge of the following, my chemistry-with-biochemistry classes were 25 years ago and I continued on to a different degree-level education that was neither chemistry nor biochemistry.)
If T production is suppressed, but not eliminated, and what T there is still has the mechanism to convert to DHT then it's possible that the further mechanism to 'disarm', 'dismantle' or further down-convert the DHT is throttled up/down by the T levels, not the DHT (biology being what it is and often uses slightly more complicated feedback loops than we might have designed it with).
Because if history has taught the evolving human body one thing, it may be that a slowly reducing level of Testosterone ought to immediately slowly reduce the removal of (soon to reduce by lower input) DHT, rather than wait for the production lag to kick in, all the better to oil the wheels of the human body at that time in life.
Or, because evolution tends to care less about what happens once reproduction starts to tail off, it's actually more a mechanism for the ramping up stage, in puberty. Rapid rises in T means rapid rises in DHT shortly, thus get the DHT-targetting enzymes ready now, lest that product spike in awkward ways before their moderation mechanismd detect them and start to kick in.
All of which makes sense in (most) natural bodies, but is a complication that medical intervention really needs to understand before trying a single-target artificial adjustment of just one (or one 'level') of the modern bodily 'humours'. Like messing with just one or two valves on a multi-product chemical synthesis plant's spaghetti-pipework and not anticipating a knock-on effect down a different feeder pipe that's now at a higher flow-rate or pressure.