I don't understand why the UTC second needs to be tied exactly to the TAI second. Define a tick to be 210 cycles of the frequency of photon absorption by transitions between the two hyperfine ground states of caesium-133 atoms, or about 22.84438 nanoseconds. The TAI second can then be defined as 43774437 ticks = 9192631770 cycles, while the UTC second can be defined as 43774438 ticks, i.e. one more tick. This would lengthen each day by 22.84438*86400 = 1973754 ns or about 2 ms. This would have the same effect as 1 leap second every 437.74437 days, but without its disruption.
The difference amounts to 83 seconds. That is, if UTC seconds continue to equal TAI seconds, by 2135 UTC will be 83 seconds ahead of where it would be with the extra tick per second.
Now TAI might not have advanced 83 seconds ahead of UT1 by 2135. If that's to be expected then a tick could be defined as a smaller divisor of 9192631770 such as 105, 126, 141, or 147; for example 147 cycles in a tick would have the same effect as 1 leap second every 625.3491 days. The proposal of no leap seconds between 2035 and 2135 would allow UTC to drift further from UT1 than any of these choices.
The criterion for whether to use TAI or UTC seconds in any given application could be something as simple as whether the periods of interest are shorter than a second (for TAI) or longer than a year (for UTC). Periods in between these two limits can use either as appropriate. In practical applications it is unusual to encounter a range of periods that includes both subsecond periods and multiyear periods, but those cases always have the option of using TAI seconds.