Inquires are not a big deal as long as they don't get out of hand. Those that have been on your report over 1 year will not contribute to your fico score, and inquiries over 6 months old weigh less on your score. Your reports will show record of hard inquires for a maximum of 2 years from the date that the inquires were made. Generally, number of inquiries should not be a determining factor when it comes to requesting a CLI or not. You may have a higher score if you wait for them to fall off but the difference will probably be very small.
Requesting a CLI may add a hard inquiry to your credit report. Different companies have different policies regarding this. Some soft pull, some hard pull.