To tackle such an important question, we will first start with the facts, followed by various options a developer has when choosing whether to have the minimum supported version as low as Gingerbread or not. For the app to support Android 2.3 and up and still bring a good UX (which stands for User Experience) in order to sway people into installing it, developers must use various tricks and workarounds, as well as putting more effort in the development process.
Why should you
The hassle of bringing your app to 2.3.X users has a positive side. The latest statistics provided by Google's Play Store still shows that a rather big chunk of the market is made of Gingerbread users.
44.1% of all the users of the Play Store, which is without a doubt the largest Android market in terms of both number of apps available and serviced clients, are still using Gingerbread-powered Android phones. If your app will support Gingerbread, you will be able to target 90.4% of the current market. If you have the means and the time or money, you can go as far as 2.X, covering 99.8% of the market. That is some plus side, compared to just 45.1%.
I'll cover some of the workaround available further down.
Why shouldn't you
Well if you think about it, phones that run Gingerbread are usually at least 2 years old, not to mention phones that didn't get updates and got stuck at Froyo or Eclair. Having said that, even though pre 4.X Android versions still make up more than half the market, this will change soon. An Old phone with Android 2.X will be exchanged sometime soon with a new shiny Jelly Bean device.
More and more people are starting to considering buying a tablet. Android tablets cover just about every corner of the market, from less than $100, up to the high-tier $700+. A friend of mine bought himself a new tablet running Android Ice Cream Sandvich with just under $75 (or â‚¬57). That was cheaper than buying an Amazon Kindle and he just wanted an entry-level tablet to browse the Internet and read brooks on. And there are more people like him that eventually will consider a tablet a good investment.
Some researchers think that Android Gingerbread will go all the way down by the end of this year. I, on the other hand, don't think that this will happen in such a steep manner. It will definitely take a good kicking this year, but people are also stuck with older phones because they don't afford to buy a new one, or are waiting for their contract with the operator to end to buy a new one.
Working with previous versions
Well if you decide to take the hard way, but not that hard of a way, you are put in front with new challenges when making the app. On one hand, you can have an app with two different functionalities each made especially for its platform features and design-wise (e.g. Google's apps like Gmail, Maps, etc.).
On the other hand you can use a library that can be used to emulate functionalities of the 4.0 and up API when called on devices pre 4.0, and get out of the way when used on Android ICS and up. One such example is the open-source ActionBarSherlock. ActionBarSherlock offers support to devices starting from Android version 2.X. Google also offers a solution for this conundrum Their support library currently at version 4, supports devices as low as Android 1.6 Donut.
In the end, it all comes down to the developer where he puts his bet. As a user stuck at Gingerbread 2.3.7 with plans to buy a new phone, I'm in that 44.1% of Gingerbread users. When I find an app I want to download on my phone, but I get turned down because of my app version, I am disappointed in that developer for not making an effort. So I turn my back to them, and look into their competition to find one that would work for my phone.