You know, I would really like to play a game that you have designed, and I'm not being sarcastic. I really would enjoy it. I think that most of us here would like a challenging, well thought out game that works properly.
It's too bad that you weren't the project manager on Civ5. It might be worth playing if you were.
I've thought of doing it, but I have no programming experience so my ability to do these things (or earn a position which can manage people who do so) is curtailed. There are lots of places game design can go wrong though:
1. Game rules/objectives/etc ----> historically civ has been very good here. Before anything else the concept of the game has to be viable or it's very hard to make a good title. The answer to what makes a title "fun" is a very difficult one to answer, even for experts and the market itself (for fun, make a poll and ask people to say why this game is fun, you'll get a lot of different answers...but not all games adapt well to multiple approaches like that!) For civ, I feel like the amount of choices available, the sense of scale, and the long term/short term strategy dynamic coupled with a connection to something people can readily identify (history, empire building and the like are common enough themes in entertainment). There's a good bit of (ability scale-able) challenge and a variety of approaches...these things are good enough to help civ overcome a lot of flaws.
2. Actual Function -----> This is, too often, lost when pushing the above. Early NES games suffer this the most, as some are not playable (same as civ V mp). This also includes bugs, broken controls, and everything else that inhibits one from interacting with the gameplay itself. Civ has historically been terrible here. The ability for players to seamlessly connect to the gaming experience is very important.
3. Project Management ------> I've had a few courses on this in grad school. Simply put, this is a rather difficult field to do well in as a manager and the pitfalls can be immense. Simply building a project plan without major conflicts and proper utilization of physical and human assets is a chore. Planning for contingencies (to the extent possible) on a reasonable cost/benefit basis, choosing the right amount of actual hirings, hiring the right people, tightening the process of design such that it's structured enough to give people a chance to do well, and somehow juggling budget ranges from a big challenge to a nightmare. I'm an arrogant person to some extent, so I think I can do it better than most

(I handle stress, particularly but not limited to time pressure, very well and tend to be very pragmatic when it comes to getting things done...and project management needs a heaping helping of pragmatism). I'm not stupid though, I'd need some heavy actual experience or a tremendous amount of luck to not screw up such a large undertaking as game design at the level of a major flagship title, such as civ V was (is? I still feel it's in a beta state

).
Programming adds another layer too. Similar to engineering projects, do you hire a project manager that is really good at programming, or one that is experienced with the reality that is project management? Non engineers have botched construction projects to the point where people have died in the past (a better manager would defer to expert experience and not try to rush the project at the risk of human safety, but I digress....). However, people put in that role lacking project management often get their projects abandoned or wind up ridiculously over-budget and taking forever because they have unrealistic estimation of how long things will take, how many people they need, that things will go perfectly, etc. Finding a project manager that has in-field experience but is ALSO personable and competent at project management itself is of course ideal. Good luck though...those people aren't common

.
Nobody will die in programming hopefully, but when you have cross-company project pressure (especially with ignorant fools like mr 2k "turn based strategy is old and unpopular, we're making xcom a shooter now and gamers need to adapt") it's easy to see how even small unforeseen complications can result in disaster. The right answer here isn't easy. As a player, I'm annoyed that firaxis/2k chose to stain their name by releasing a beta, but I'm cynical and I've been trained to think in business terms:
1. Despite it being a shoddy product and far from being complete, a large portion of the market accepted civ V beta public sale release with open arms and still do so.
2. My guess is that they (accurately) estimated that the title would do very well in sales regardless, and projects do cost money to continue to refine...
3. 2k's recent public statement make me wonder very much their intention of releasing or even bothering to develop another flagship TBS. If for whatever reason management decides tbs are not going to be viable long-term, deliberately releasing an unfinished product and milking max money before dumping the studio or changing the series entirely makes business sense...especially when you can get a mixed or even somewhat positive public response in the past (or pin the blame on developers with their hands tied!). I'm not saying this is what happened because I have no idea of the relationship between firaxis/2k or either's long term plans, but my point is that there are viable, if cynical, arguments for firaxis/2k to behave in ways that are overtly unfavorable to gamers who want a complete and fluid experience.
4. The specific project management design goal could therefore have been on a profitable game rather than a great one. In business terms this trades long-term reputation effects and customer loyalty (which *is* profitable) for short term income...very viable if you don't think long-term prospects good. Could I make a good game in that environment? Could anyone? It would be very difficult to do it. Ironically, this is not unlike some decision making in civ itself...you get loyal allies and milk them until it looks like they can't be useful anymore...and then they'd better watch their backs

.
Nobody in business will ever word it that way, but actions reflect the reality. Time will tell 2k/firaxis choice very well.
TL : DR
Could I make a good game? I believe I could, but it would be difficult to do it alone. Even games that were essentially start-ups like minecraft have continued to add things over time with increasing help/suggestions/implementations from others. It's an interesting model though, one I might have considered if I'd have gone the programming route in schooling...but then I'd be lacking a lot of the skills I currently possess. Don't tempt me to go back to school X_X.