Ammo is a consideration in real life because the emphasis is placed on suppressing the enemy force through massive volumes of fire, and because typical engagements involve high numbers of enemy units and at longer ranges.
Some reasons why this doesn't occur in Xenonauts:
1. Single shots are emphasized, and strong. Rifleman in the military are supposed to fire in three round bursts as a general rule and fire single rounds when accuracy is paramount. A twenty-round magazine goes by relatively quickly when you fire the rounds three at a time rather than 1.
2. Burst fire costs too many TUs. In real life, firing a burst doesn't really take any more time than firing a single shot; you acquire the target, burst, then reacquire for the next shot. Ideally I would like for the game to allow for snap, normal, and aimed burst-fire in addition to snap, normal, and aimed single fire; ideally all for the same cost but at differing accuracies.
3. Suppression through volume fire is relatively de-emphasized. It appears to be tied to accuracy of the rounds; in effect, this magnifies the value of the high-percentage single shots which deal more damage and also suppress more often. In reality, suppression is typically effective as long as you are firing in the general vicinity of an enemy unit. Obviously hitting an enemy has the most suppressive effect, but you typically can't tell how close bullets are to hitting you; anywhere within 5 meters and you'll be suppressed. This is especially important during 0-4% shots taken from a machine gun (either taken at beyond the weapons effective range, or taken at a target hunkering down in cover); you should still want to take them because you want the enemy to think that if they stick their head up from cover, they'll take a bullet to the face.
4. The engagement ranges are short. Longer sight ranges forces you to take cover earlier and fire lower-percentage shots, which means you'll expend more ammo.
5. Cover collapses too slowly to volume fire due to the absurdly inaccurate sprays it produces. Volume fire, in addition to its suppression effects, should also hit cover more often than it sprays ineffectually at the ground around the enemy, in order to destroy the cover quicker. With these two benefits, single shots can be tuned toward being more likely to deal more damage than burst fire (e.g. a single shot at 10% accuracy or three shots at 98% accuracy favors the single shot in average damage output; similarly, a single shot at 60% accuracy or three shots at 85% accuracy favors the single shot in average damage output), while burst-fire and machine guns have high suppression and destroy cover quickly.
6. Units can easily flee out of your sight range in between turns. The progress you made towards maneuvering a suppression element into position or destroying their cover is effectively negated. This encourages you to spend your ammo on better-percentage shots and outfit your soldiers likewise (by massing snipers, for instance). This is mostly a result of the poorly-implemented suppression mechanics; if suppression were more common during volume fire, the enemy would be forced to hunker down for several turns, allowing for you to tactically maneuver a flanking element and also allowing for large expenditures of ammo.
7. Overall engagement sizes are low. This ultimately isn't going to change much in the future, I imagine, since the enemies are tuned to be highly lethal.
While all these factors need not be changed at once (indeed doing so might make burst fire too powerful), at least a few of them must change for volume fire to be a reasonable option worth considering.
Personally, I disagree with effectively removing the strength stat from the game. A better option is to fine-tune the scaling on the weights of higher-tier weapons, armor, and equipment and the growth rate/cap of the strength stat to create the same effect; you experience tradeoffs in the early game since you have a low overall weight cap, and you experience tradeoffs in the end game through balancing the benefits of upgrading with the corresponding weight. Removing game mechanics (even something as simple as the increase in carrying capacity over time) should be a last resort.