I don't understand the how "strict alternate picking" is useful. If you have to focus on every stroke, and even go against your natural tendency sometimes, it's probably a bad idea. Economy picking is considered bad sometimes because it's harder to play the correct durations with it, but strict alternate picking can feel confusing an unnatural sometimes.
Also note that if you play two consecutive downstrokes or upstrokes it doesn't necessarily mean that you're economy picking. Economy picking is when you hit one note, then another one within the same upstroke or downstroke. If you use two downstrokes in succession it's not economy picking.
The technique that feels the most natural for me is to keep a steady 16th note up and down motion with my right hand, and only hit the string with the pick when I need to. It's like tremolo picking but, but you keep the pick away from the strings on rests or in the middle of notes longer than 16ths. With this method it's hard to mess up the rhythm, and it feels extremely natural. The hard part is learning not to hit the strings by mistake when you don't need to.
So to answer your question, sticking to alternate picking 100% of the time can be bad. It's ok to break up the pattern on rests or any note longer than a 16th if it makes you comfortable. Ultimately you want a technique that maximizes your accuracy and speed. A confusing picking technique (like pure alternate picking) doesn't help much in this area. While economy picking can help with speed, it doesn't help with accuracy. So it's ok to use it in a short lick that would be a bit too fast for alternate picking. You need to experiment with every possible picking technique and understand it's advantages and disadvantages. You've tried economy picking, strict alternate picking; now try to play alternate picking your way (break it up whenever you want but do not hit two consecutive note with the same motion), also try the technique I recommended above (players like Jimmy Hendrix and Stevie Ray Vaughan use it a lot). You probably should combine these techniques depending on the scenario, instead of constraining yourself to the same rule the hole time.