I have to disagree. A lower strike rate is not so useful if your not even going to bowl him much. Someone with a higher strike rate and a lower economy rate is going to be more useful to the team if your always bowling him long spells compared to the higher strike rate player whom you are only giving short spells.
While there is nothing wrong with having a low strike rate there is also no excuse for having a high economy rate. You are costing/hurting the game for your team if you are giving away too much runs.
The problem here is that you are looking at this from an isolationist perspective. You are looking at a single bowler and what they do. But the thing is that batsmen face two bowlers at any one time. Let's look at a hypothetical situation:
Bowler A has an economy of 4 and a strike rate of 30
Bowler B has an economy of 2 and a strike rate of 60
Bowler C has an economy of 3 and a strike rate of 60 and is bowling in tandem with either A or B.
Let's pretend that this is an ideal world and everyone takes their wickets at the last ball of their strike rate.
A and C bowl together.
After 10 overs:
A - 5 overs, 1/20
C - 5 overs, 0/15
Opposition team - 1/35
After 20 overs:
A 10 overs, 2/40
C 10 overs, 1/30
Opposition team - 3/70
B and C bowl together.
After 10 overs:
B - 5 overs, 0/10
C - 5 overs, 0/15
Opposition team - 0/25
After 20 overs:
B - 10 overs, 1/20
C - 10 overs, 1/30
Opposition team - 2/50
The bowler with the faster strike rate but the same average has gotten the opposition team to be 3/70 after 20 overs instead of 2/50. Now in both cases the bowling team could said to be on top and this is a very contrived example, but the point remains that if you have a low average, having a low strike rate is way more beneficial than having a low economy.
So continuing with our situation, let's add bowlers D and E to the situation, both of which are brought on after the opening 20 over spell. They both have an average of 40 and a strike rate of 60. They get 10 overs each.
After 40 overs:
A & C - Opposition are now 5/150
B & C - Opposition are now 4/130
The bowlers continue operating in this way until the entire side has been dismissed.
A & C - Opposition are dismissed for 300 after 80 overs
A - 20 overs, 4/80
C - 20 overs, 2/60
D & E - 20 overs, 2/80
B & C - Opposition are 8/260 after 80 overs and are dismissed for 310 after 100 overs
B - 30 overs, 3/60
C - 30 overs, 3/90
D & E - 20 overs, 2/80
So just by one bowler having a better strike rate than a bowler who has an identical average but worse strike rate, the first side has dismissed their opposition for ten runs less, have spent 20 overs less in the field and their main strike bowlers have bowled 20 overs each instead of 30.
Of course this is a contrived example to show the mathematics of why, given identical averages a high strike rate is better than a low economy rate. This is only true though if your lowest averaging bowler has the best strike rate. For bowlers with high bowling averages the reverse is true. You basically want your attack leaders to be striking fast with little to no regard for their economy. You want your support bowlers to have a lower economy rate as that gives you more opportunity to expose the opposition batsmen to your better bowlers.
Also, this is only applicable to tests, where you must take 20 opposition wickets to win. In ODIs you have a lot of other considerations and economy is far more important.
Your argument about shorter spells is an interesting one, but only if they are bowling less overs in comparison to their strike rate than the slower bowler. In reality most bowlers in modern test match cricket bowl a similar amount of overs, which again, favours the bowler with the better strike rate.