...India didn't do this with the LCA. They should do it with Kaveri, but I am afraid there are just too many people and politicians who would turn this into a patriotic debate, saying somewhat along the lines of what you have claimed, "believe in the Indian scientific community. We can go to the moon, so we can build an engine". No doubt you could, but at what cost? Almost half the country is below the international poverty line, it only makes sense to stop throwing money down pits.
LCA and Kaveri are the first steps India took for indigenous fighter aircrafts and engines. To me these are very important steps for a country that want to be less dependent from others and don't want to be only a buyer. In the helicopter field India is already ahead with Dhruv, Shakti engine and now new onwn developments like LCH and LOH. The aircraft field is catching up and they will learn from the problems they faced. All these experience will be a benefit to later developments and jv that India will have in future, be it indigenous, or partnerships with other nations.
About Kaveri, the problem is definitely not the thrust, it already would fulfill PAFs requirement for JF17 engine, but IAF seems to have other requirements. That's also why they didn't go for Russian (RD 33/93), or French (M88) engine for LCA MK2. There is already a jv with Snecma to fix Kaveris problems and the new engines for LCA MK 2 could come with ToT too (some reports are talking about it). So IAF and MoD are doing everything to solve the problems and get it done and that is imo crutial!
You can't go on and improve yourself if you didn't end what you have started.
LCA and Kaveri might be delayed, but they can't be failures, if we bring those projects to the end. And that is what happening now, instead of many not mature MK1 versions, that have to improve and upgraded through the years, there will only be 2 squads (mainly for training pilots) of them. The more mature MK2 version will come in numbers and with more capabilities only, that is the best way out of the problems.
Btw, if you look at LCA and other fighter projects you will see the same problems and delays too and those countries have way more experience than India. Look at EF 2000 for example, development started in the mid 80s and it is still not fully developed and facing several delays and problems too! Rafales M88 engine was not ready from the start too and they used also the GE 404 for their demonstrators and prototypes for nearly 10 years.