Which light fighter from Russia? They do not have any modern (4+ gen), single engined light aircraft. Ditto for US. The F-16 with all the latest goodies is a medium weight fighter, which is why it competed in the MRCA competition. We badly need a cheap, light weight fighter - otherwise our force structure is getting unaffordably imbalanced.
Of course if we had paid for the development of a cheap and light fighter, I'm sure USA or Russia could have made us one. But why would we pay money to support their research, instead of spending a fraction of that amount domestically? Bear in mind that the entire cost of the LCA program over the past two decades has been a small fraction that Europe spent on designing Rafale or Eurofighter. The cost benefit ratio has been huge.
The goal of LCA was to develop a modern, indegenous fighter. How would that goal be served by purchasing from abroad?
Another point to note is that the reason for having a light fighter is to keep costs down, both aquisition as well as operational. The LCA is only expected to cost approx $25-30 million per unit, despite having American engines (which contributes a lot to the cost), even though we will only make around 200 of them. F-16s, even with a production run of several thousands, costs more. If we ask the US or Russia to manufacture a light jet for a production run of just 200, imagine how expensive it would be - designing plus manufacturing.
So no, when we emarked on the LCA project, that was the only way for us to develop an indegenous aviation industry. And today, despite all the delays, it is still our only option to sustain squadrons strength cheaply.
I wonder who bombed the living daylights out of Pakistani terrorists and special forces in Kargil in 1999. I wonder who flew recon missions with mig-23s, who bombed each peak with PGMs quickly integrated on Mirages, who flew mig-29s as fighter escorts and kept Pakistani F-16s away in fear.