I'm happy with the firing patterns as they are but just want to say that staggered firing isn't necessarily always bad. Other games implement it not just for visual or aesthetic reasons, but for actual gameplay mechanics. As stated in previous replies, there will be added complexity in maintaining/balancing the firing rate and DPS, but it can be done. It will require distributing the firing rate across the number of hardpoints each type of weapon is equipped under.
This debate has appeared in other games as Volley vs Ripple fire, where Volley represents all weapons firing simultaneously in unison and Ripple represents staggered or sequential firing. Under ideal circumstances (i.e. where aim and trajectory are perfectly determined), volley fire will maximize the damage inflicted and minimize the time to kill. In contrast, when the target has not been perfectly "locked in" or the target is significantly agile, ripple fire allows firing to be continuously adjusted so that more shots land on the target. Instead of every shot either hitting or missing, some shots will connect while others will not.
Another advantage of ripple fire is that it doesn't commit all weapon resources with every firing execution, so resources can be preserved for additional targets. If a weapon is capable of one-shotting an enemy, and you have 4 of that weapon equipped against 4 of that type of enemy, then ripple fire will allow greater flexibility in eliminating those threats if you fire conservatively. Volley fire, on the other hand, will unnecessarily consume resources from every weapon with each target fired upon, in turn prolonging the engagement as more time will be required to reload or cool down weapons.
To borrow again from Everspace 2, below examples illustrate how these two types of firing methods can be practically implemented for projectile and beam weapons alike.
Projectile and beam weapons firing in sequence (Ripple fire)
Alternate weapons firing in unison (Volley fire)
However, it needs to be clearly noted that it would not be trivial to implement this feature. Aside from the development effort involved, there would need to be careful design decisions, such as which weapons would fire under which methods and how would the player be given control and how much control would players receive, etc.