Bowling SR is more valuable because you need 20 wickets to win a Test match with limited time. 450 maximum overs (90 x 6) with your team getting ~50% of that. 225 overs to get 20 wickets - this is why SR is more valuable than Econ. 225 * 6 / 20 = ~67.5 SR needed to win game.
Consider these 2 hypothetical bowlers:
25 average, 60 SR, 2.5 Econ
25 average, 75 SR 2 Econ
^ Both of them have the same average, but if your bowling attack all had a 75 SR like the 2nd bowler you would on average not have enough time to get 20 wickets assuming you had ~225 overs to get those wickets.
Batting SR is just nice to have but it is not as essential - as long as you hang around you will get runs. Since a Draw is a viable result in a Test, Batting SR is just not as important as it would be in limited overs formats.
I think Davidson has one of the highest strike rates for an ATG bowler and his Strike Rate is 62, which is below the strike rate needed to win. I don't think it's as big of a concern as you make out.
Other high SR Bowlers with averages under 25 (wickets @ average in brackets):
Ironmonger 63 (74 @ 17.97)
Wardle 64.6 (102 @ 20.39)
Davidson 62.2 (186 @ 20.53)
Toshak 66.8 (47 @ 21.04)
Adcock 61.4 (104 @ 21.10)
Laker 62.3 (193 @ 21.24)
Peate 67.6 (31 @ 22.03)
Hearne 60.07 (49 @ 22.08)
Attewell 101.7 (28 @ 22.35)
Loader 68.2 (39 @ 22.51)
Barlow 72.2 (34 @ 22.55)
O'Reilly 69.6 (144 @ 22.59)
Kline 69.7 (34 @ 22.82)
Miller 61.5 (170 @ 22.97)
Jadeja 61.6 (142 @ 23.12)
Sajjad 70.2 (59 @ 23.89)
Johnston 69 (160 @ 23.91)
Grimmett 67.1 (216 @ 24.21)
Verity 77.5 (144 @ 24.37)
Mahmood 70.7 (139 @ 24.70)
Statham 63.7 (252 @ 24.84)
Bedser 67.4 (236 @ 24.89)
Almost every single bowler on that list who has taken over 100 wickets is recognised as an all time great. Most of them have strike rates that are more heavily impacted by the era in which they played than their skills with the ball. Lindwall just missed out on this list with a strike rate of 59.8. Nobody would suggest that an attack with Lindwall, Miller, Davidson and O'Reilly isn't good enough to win a majority of tests.