The fact that defensemen were considered from the Hart through WW2 but barely got considered afterwards made it more difficult (relatively) for forwards from this time period to receive Hart consideration
This post has every Top 5 Hart finish by a defenseman in NHL history.
From 1924-1946, at least one defenseman finished top 5 for the Hart in every season but two and multiple defensemen were top-5 13 times in the 23 years. From 1947-1966, only Kelly and Harvey ever finished top 5 in Hart voting, and things didn't get any easier for defensemen afterwards.
Here is every top 5 Hart finish by a defenseman during the primes of Beliveau, Mikita, and Messier:
Beliveau: 1955-1966
1954-55 5) Doug Harvey
1955-56 4) Red Kelly 5) Doug Harvey
1956-57 5) Doug Harvey
1957-58 3) Doug Harvey
1961-62 2) Doug Harvey
Mikita: 1962-1970
1961-62 2) Doug Harvey
1966-67 5) Harry Howell
1967-68 4) Bobby Orr
1968-69 3) Bobby Orr
1969-70 1) Bobby Orr 5) Brad Park
Messier: 1987-1997
1986-87 2) Ray Bourque
1989-90 2) Ray Bourque
1990-91 4) Ray Bourque
1994-95 4) Paul Coffey
Now Morenz: 1924-1933
1923-24 2) Sprague Cleghorn 4) Georges Boucher
1925-26 2) Sprague Cleghorn
1926-27 5) King Clancy
1927-28 3) Eddie Shore 5) Ching Johnson
1928-29 3) Eddie Shore 4) Sylvio Mantha 5) King Clancy
1929-30 2) Lionel Hitchman 4) King Clancy
1930-31 2) Eddie Shore 3) King Clancy
1931-32 2) Ching Johnson 4) Red Dutton (we only have the top 4)
1932-33 1) Eddie Shore (we only have the top 4)
If you "remove" all defensemen who finished ahead of Morenz, he would have at least 8 Top 5 Hart finishes, only 1 fewer than Jean Beliveau, and well ahead of any center but Gretzky/Lemieux/Beliveau
These aren't insignificant 7th/8th place finishes, due to serious vote splitting during the era, Morenz received a large number of votes. For example, when Morenz finished 8th in 1927, he had 30 voting points, to 89 for 1st place. When he was 7th in 1930, he had 60 points to 101 for 1st.
year|actual finish|no defensemen
1924|6th|4th
1925|2nd|2nd
1926|6th|5th
1927|8th|5th
1928|1st|1st
1929|NA*|NA
1930|7th|5th
1931|1st|1st
1932|1st|1st
1933|?|?
*We only have the top 7 for 1929, Morenz wasn't top 7
? In 1933, when Morenz was a 2nd Team AS, we only have the top 4, Morenz wasn't top 4. 1 of the top 4 was a defenseman.
Note that even if you remove every defenseman but leave in Shore (since he'd get Hart votes in any era), the table above is unchanged (since Morenz beats Shore twice anyway and Morenz isn't ranked in 1929, the only other season Shore shows up before his 1933 victory.