Think about it like this- whats more interesting: playing a game where you move your mouse over 2 points to gain points, or a gain where you just watch you points grow.
I'm not saying it's the best mechanic in the world, but I'd rather it be something rather than nothing. My game isn't too fun anyway so it's a bad example to use, but it adds to the hectic feeling of defence games, where your having to manage between upgrading your base, killing enemies and gaining income.
But yes, its a badly thought out mechanic.
I'm not going to belabour this point much further, since I think both of us understand it pretty well. This is a test game, so it's unfair to rip into it to the full extent.
I will say this; if removing a boring mechanic will make the game feel empty, that's a sign that you need to rethink the core design. You should understand what your game is about. The most important question is "What does the player DO?" Every single part of the game must aim toward that purpose.
In your case, it sounds like you want a game that's focused on reflexes and fast resource management. That's a decent thing to focus on, so let's imagine possible ways to do this. There are many games that use time as a resource - many puzzle games are timed. Tetris, for example, would lose its charm if you had an hour to think things over. The key is giving a player a problem that he barely has enough time to solve.
If you want resource gathering to be constrained by time, I would suggest thinking of something more challenging as the resource gathering activity. How about a simple skill-and-action game, or some sort of spacial puzzle? For example, you could create random wandering creep monsters that the player has to click to beat coins out of them. That way the player's brain is engaged at all times and the action will feel MORE hectic.
I don't know how far you want to take this, but I would encourage you to tune and balance this game. It's not going to win the IGF prize for design, but it will teach you how to polish a design into something interesting. The basic elements are already there - you could make it into a fun 10-minute clicker. Anyway; it's your choice, obviously. Maybe you have the next IGF winner as your next idea
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I should learn Flash; then I would be able to throw something together quickly as an illustration. C++ is too cumbersome for these things.