I believe that Knuth himself gives an answer in “The Art of Computer Programming”.

He says:

High level languages are inadequate for discussing important low-level
details such as coroutine linkage, random number generation,
multi-precision arithmetic, and many problems involving the efficient
usage of memory.

But the decision to use a machine-oriented language is probably due to the fact that:

New algebraic languages go in and out of fashion every five years or
so, while I am trying to emphasize concepts that are timeless.

^{(Preface to TAOCP vol. 1)}

Moreover, if I did use a high-level language, what language should it be? In
the 1960s I would probably have chosen Algol W; in the 1970s, I would then
have had to rewrite my books using Pascal; in the 1980s, I would surely have
changed everything to C; in the 1990s, I would have had to switch to C++ and
then probably to Java. In the 2000s, yet another language will no doubt be
de rigueur. I cannot afford the time to rewrite my books as languages go in
and out of fashion; languages aren’t the point of my books, the point is
rather what you can do in your favorite language. My books focus on timeless
truths.

---

Expressing basic methods like algorithms for sorting and searching in machine
language makes it possible to carry out meaningful studies of the effects of
cache and RAM size and other hardware characteristics (memory speed,
pipelining, multiple issue, lookaside buffers, the size of cache blocks,
etc.) when comparing different schemes.

Indeed since ’60 there were suitable notation for coroutines in ALGOL-like languages:

…coroutine linkage had already been noted briefly as a “programming tip” in
an early UNIVAC publication […] A suitable notation for coroutines in
ALGOL-like languages was introduced in Dahl and Nygaard’s SIMULA I […] and
several excellent examples of coroutines (including replicated coroutines)
appear in the book Structured Programming [by Dahl, Dijkstra, and Hoare].

^{(TAOCP vol. 1, pp 229-230)}

Not to mention high-precision / multiple precision routine in FORTRAN / ALGOL:

Extended precision subroutines for use in FORTRAN programs were described by
B.I. Blum (1965) […] and for use in ALGOL by M. Tienari and V.Suokonautio
[…]
Arithmetic on integers with unlimited precision, making use of linked memory allocation techniques, was elegantly introduced by G.E. Collins […]

^{(TAOCP vol. 2, pg 279)}

Same about random number generation: there are examples in C (TAOCP vol. 2, pp 185-188) and exercises in other high level languages (e.g. [EX10] pg 193).