MySQL 8.0.30

i have three tables defined

C, CT, T

CT is a linking table (many-to-many between C & T)

The query i'm trying to optimize is of the following kind:

SELECT C.*, T.*
FROM C JOIN CT ON C.id = CT.cid JOIN T ON CT.tid = T.id
WHERE T.col = 8
ORDER BY C.pop
LIMIT 20

There are secondary indices defined on T.col and on C.pop

The optimal query plan is to satisfy the query with the following join-order:

C (*using C.pop_idx*)
join CT (c.id == ct.cid)
join T (ct.tid == t.id)
filter (T.col == 8)

There is no doubt that this is the optimal query plan (because of the ORDER BY and LIMIT clauses)

What MySQL chooses instead is:

CT (table-scan)
join T (using T.primary)
filter T.col == 8
join C (using C.primary)

I've tried everything I can think of: using FORCE INDEX, query optimizer hints

(/* JOIN_ORDER(C, CT, T) */), /* INDEX(C, C.pop_idx) */, etc, etc

But to no avail

The frustrating thing is that I've seen query plans where MySQL is smart enough to do exactly what I want it to do, viz. use the index defined on the ORDER BY/LIMIT to "filter" the rows in the outermost table as the outermost loop of a nested loop IJ, but I simply can't induce it to do so in this case Any ideas?

for those interested (not necessary to answer question): the calculations as to why said query plan would be optimal: pseudo-code:

for each row in C [using index C.pop_idx read 20 rows (or so) in order at a time]
     for each matching row in CT (CT.cid == C.id) (using CT primary)
          for each matching row in T (CT.tid == T.id) (using T primary)
              if T.col == 8:
                   emit C.*, T.*
    
              if total emitted rows == 20:
                  done

even if the % of T rows with T.col == 8 is small (say, 1%), on average only 20 * 100 C rows would need to be read (which is way less than all the rows in CT)