At variable prices, revenue-redemption rewards programs (especially bank-based airline-independent ones) can get you any seat that anyone is willing to sell on any airline, but then the higher the cost of the seat in money, the higher the cost of the seat in those points, no way around it.
So you never should simply ask just whether there's award availability. You should also ask at what cost. Because in some cases, especially with revenue-based rewards, there is always award availability (as long as there are seats for sale*) but the cost can skyrocket to the point where most people wouldn't consider it a good value and where most people wouldn't have enough of those points to redeem for that anyway**.
So if there isn't award availability, I should be able to pay cash to make up the difference? That's probably not what you mean but I'm not grasping it.
Unless you're earning some of your points in non-linear ways (ie, through bonuses not proportional to spend), most revenue-based redemption methods of getting to "anytime" seats work out no better than typical "cashback" credit card returns, sometimes even worse.
That isn't what I've found at all. For example, last summer I booked two first-class one-way direct-flight tickets from LON to SFO with a United Standard (non-Saver) Award for 295K miles at the last minute. At the time, united.com said the tickets would have cost over $20K each. I just searched for the same tickets on the same date this year and the total cost of both is currently $27,569. With my United credit card, earning 295K miles means spending $147,500 which would earn $2,950 cash back at 2%. There's no comparison.