I had this Idea yesterday when I couldn't fall asleep. First I need to define the problem or rather explain what aspect of that question I want look at.
The scenario is I am on a navy map where I build up my base end eventually decide to build a navy factory and build a frigate which I send towards my enemy. I have an income of lets say 58 mass/per second so the factory and the frigate take up 10 seconds of my mass income. That frigate is now going to the enemy base killing some engies trying to build a navy factory. The frigate takes 100 seconds to reach the enemy base. So the question how much mass worth in engies would that frigate actually need to kill to be worth it? Here I am going to only look at economy damage and also ignore reclaim. (You can add that if you want to but it doesn't really change the concept I am going for). Also I am ignoring potential navy locking and the following additional costs my opponent would need to get back into the pond.
So lets say my opponent has the same income as me when I am building that frigate (58). If he is just ecowhoring for the next 100s. Also I will not bother with the exponential scaling of his economy and extrapolate his income linearly (minimum estimate). So 58 m/s100= 5800. That is about 6 t2 mex. So by the time my frigate arrives he would have 58m/s+46m/s=82m/s.
Now my model is that I would need to set him back more than 10s of his mass income to make the investment worthwile. That would mean the frigate would need to kill 820 mass to set him back more than it set me back. You could also call it pay for itself.
This example was an attempt of quantifying the negative travel time impact of any unit going on a raid.
Seems like you answered your own question! If these thoughts continue to bother you then you should consider seeing a therapist.
cost of a frigate (250) + Naval Yard (300) is 550, that's ~60% of t2 mex. Let's say both of you have 50 m/s income, if you invest the mass in frigate + Naval Yard and your enemy into t2 mexes then by the time your frigate would arrive to deal dmg (100s travel time) his mex would generate (ignoring compounding) ~93 * 4 = 372 mass so that's around the dmg your frigate would need to do. However if your frigate manages to only kill 4 t1 mex and deny them for 100s then after 200s after the frigate was made your eco situation would look like: Player 1 (with frigate) 0 * 100 + (+4)*100 =400 vs Player 2 (mexes) (+4)*93 + 0 *100 = 372 so Player 1 would be ahead (ignoring compounding).
By choosing to ignore navy locking and the cost of getting back in the pond you are ignoring the only important metric in the equation. The entire reason to send a frigate to kill navy engineers is to delay your opponents navy. It doesn't matter if they have more mass income because it will just build up in their mass bar while their engineers are dead. They either have to replace the engineers or switch to a different strategy of spending mass. You will be ahead on navy production for a long time since they have to replace their dead engineers with even more engineers to catch up. Being ahead in navy will give you numerous incalculable advantages (map control, intel, aa, reclaim, etc).
The economic damage the frigate can cause is always lower than its costs. There are some rare cases on setons wherenan early aon frigate can kill 4-5 rock mexes (2 island, one on rocks beach, the obvious forward one and one core mex) but even in those scenarios its hardly more than a nuisance.
I think i have alot of experience when it comes to timing pushes on navy and the key concept is, as thomas explained, build power denial. Ultimately most of my navy wins happen because of build power denial. You can scale up your bp, especially the one needed for a timely T2 transition, keep denying enemy bp with suicide frigates raids or plain water entry denial and then finish the game with cruiser tml or bship. Its of course vulnerable to torps, hover or any other mid intervention like drops, and stuff, but a satisfying way to show an eco whore its place. Think about frigates more as a tool of bp denial in the early stages of navy, and you will learn to use it as an efficient attack.