The short answer is yes.
Long before it was popular Nautilus (the original inventors of exercise machines) knew that good exercise contained strength and stamina in the same workout. They worked to provide equipment to make it possible to get this done in 30 minutes without sacrificing intensity OR safety.
The original Nautilus protocols were to move from one exercise to the other with minimal rest. This combined with training each movement to momentary muscular failure makes for a huge draw on your support systems to feed your hard working muscles and keep them contracting. This all before your cortisol levels become counter productive.
The mistake most make cross training is they workout in a manner which makes their heart beat like a rabbit in a race. By this we mean fast little low blood volume beats with a hope to sweat off the pounds and feel like an athlete. You want a large deficit of materials (like oxygen) feeding your muscles but you don’t want a superficial ‘racing’ heartbeat. Think deep breathing and a heart beat you can feel in your chest not shallow breathing and heart in your throat feel.
With the Nautilus method you use the full range of motion of every exercise and avoid cheating any moves by bouncing or throwing with momentum. This allows a really big draw on the blood stream and the heart makes big blood volume beats as you squeeze and wring out your muscles until they are dry.
Arnold in an original nautilus pullover machine
So again yes you should be looking to tax both your strength and stamina in a workout and for the sake of function and flexibility you should do so through a full range of motion. Just be careful to not get caught up in trying to force a sweat by pretending to be and athlete in the middle of competition. Remember exercise is activity/sport preparation and injury prevention NOT actually playing a sport.
You don’t have to sacrifice the strength portion of exercise to make it cross training in fact it lessens the effect to do so. Light weights thrown around while you bounce around may feel like good exercise but it won’t provide more than that fleeting feeling. Have fun getting fit by taking an intelligent interest in the homework and then go play with your better body.
Be well, be strong,
Andrew and Tierney