Should the company use LC facilities even if it is cash rich?

Yes. LC is used for securing your payment on time. It is the safe method of payment.

Yes. Availing Trade finance will ensure smooth flow of business transactions especially when the company deals with International suppliers.

LC covers risk for both the parties.

Letter of credit is a mechanism which ensures that goods will be delivred to importer and exporter will get the payment in return.

There are a lot of possible reasons.  The corporate finance experts will talk about the cost of debt versus equity, the dilution of ownership that will occur if shares are issued and the cashflow pressure that debt brings.  And many other relevant factors.  All of these are true.

However....

There are two other things which are much more important.  One is the relative condition of the debt and equity markets at the time the company needs the money.  What is the fastest, easiest and cheapest (in the sense of the cost of making the issue, not the long term cost of the finance itself) way of raising the money?

The other - which is the most important of the lot - is the personal prejudice of the CEO or finance director.  Some hate debt.  Some hate equity. 

Oh, and don't forget the banks that advise on, run or underwrite the issue: their advice may or may not be influenced by which is better for them.

YES , inorder to secure its payments.

yes LC will secure the trade operation either if the company sell or buy and it will make the trade process go in safe and smooth manner

Here if the meaning of LC is "Line of Credit" which is normally arranged with banks by the company for the purpose of meeting out the urgent need of funds for day to day working, then answer is a big "NO". Because the rate of interest charged on LC will always be more than interest paid by the bank on deposits.

If this LC is related to international business transactions them the answer is "Yes". As it is always safe to have transaction through LC mechanism.