Time is a problem every designer has.
I don't think I've had a single job where the client's said: "time's not an issue, just make sure it's designed well", unless I'm working for myself, in which case I hardly ever get anything finished! Hah.
The ability to design well within a set amount of time is what really separates the good designers from the bad ones IMHO, and you'll find this problem in every field. A solid design doesn't count for shit if you finished it 2 weeks after the bands CD launch. However, there are companies around that are well known for their solid design and execution of web related products. 2Advanced comes to mind. They probably charge more for their work than most and likely take a lot longer for you're average site, but the proof is in the pudding so to speak.
If you want to be a high profile designer then that's the market you need to target. Problem is, that's probably where the competition is toughest. Everyone wants to do the high profile work as this is what drives most designers passion for the industry.
From a business standpoint, this really boils down to a risk management issue. If you want high profile work you'll need to outlay a lot to get noticed, and even if you do you'll need to be good enough to attract a client base. If you're good enough to attract, you'll need to know how to handle those kinds of clients and so on...
Personally, I'd just stick to freelancing *glances at jason* there's less aspirin involved :P
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As for how I feel about this biz? Quite good.
The web and its related technologies are spawning some really interesting stuff (mobile tech rocks my world right now). Then again, I seem to get off on doing the craziest shit that no one would every rightly pay me for. I love the web, and my passion for interaction design started here, but my undergraduate years have had me branching out into other areas like multimedia installations, $0 budget video production and all manner of crazy stuff. Nothing commercially viable, but it beats the crap out of playing video games when it comes to passing the time (but video games are good too). However, I've gotten some free trips to festivals and exhibitions out of it so far so it can't be all bad.
Furthermore, whilst I'm here and I've got the skills I may as well use them to turn a buck. It's a bit of the old "can't have your cake and eat it too". But who knows, one of my experiments might turn out to be something truly useful, if not then at least I've got some employable skills to fall back on.
At least, that's the way I see it right now. I graduate in about 6 weeks. I have a broad skillet without any real specializations. I program, I illustrate, and I can make a mean cup of coffee. But above all I design. Weather it be with the side of a building and a projector or a copy of photoshop and a web server makes little difference to me. As long as I'm not doing the same shit day in day out, I'm fairly happy. I'll probably end up specializing with something at some point, but not now, not yet. There's just too much cool stuff to play with. I should point out that this goes against everything my professional practice lecturer and our industry guest speakers say they're looking for in graduates. They want specialized drone workers for their ant farm companies, but screw that. My broad interests make me a better designer. If that means the big corp. boys don?t want to employ me than that?s fine, I can make just as much money doing small freelance jobs.
Although I doubt I'll ever completely cut my ties with the web. Everything started here and whilst I've drifted away every now and then, I?ve always come back. So when it comes to making the $$$, I'll be looking for web dev jobs of some kind. The $$$ let me bake my cake, my personal endeavors and experiments is when I get to eat it.