you would be restricted to lower resolutions on a TV than you would get with a Monitor, in fact most TV's will only allow you to use a single resolution that suits the screen, and this resolution variant depending on what TV you get will be much lower than what a Monitor of equal size can offer you, unless your going for an Ultra HD model which wont be cheaper than a decent Monitor.
Also I think you are mistaken saying its cheaper to get a TV over a Monitor, because if you where to compare the 2 in terms of the Resolution that will be offered and Refresh rates, then on equal par the TV will be much more expensive, really you can't go less than 60Hz on the refresh rate, the faster the better especially if your gaming, I think realistically you would be looking around the same price for a TV that would only offer you 60, as a decent LED Monitor that would give you 120Hz, if you move up in range to a TV that will give you 120Hz then you could get a Monitor that would give you up to 240Hz for the same price, only going right up to a top of the range Ultra HD TV screen would you get 240Hz out of a TV, where as you could do this much cheaper with a good LED Monitor.
Also response times on TV's tends to be much slower, again will have an impact on gaming, a really decent TV could maybe offer you down to a response time of around 8ms even 6ms, but then you are in the realms of a very expensive TV, cheaper more standard TV models can commonly offer between 20ms to 30ms which will suck and cause blurry images when gaming, where as with a Monitor its really not that hard to find a really good Monitor that could offer you a response time as low as 2ms for a fraction of the price you would get a response time of 6ms out of a TV, even 5ms I would consider fairly slow for a Monitor, so TV's even at the high end have not been able to equal response times of a fairly average Monitor.
Really when choosing, you want to look at these specific 3 attributes
1. Resolution
2. Refresh Rates
3. Response Times
And once you start matching these attributes between a TV and a Monitor then the TV is not a cheaper option, so most Gamers especially would choose a decent Monitor over a TV to get a better spec cheaper.