Depending on the area you live in, yes, I absolutely would. Reasons:
I've studied a good half a dozen, very in demand areas*. The number of houses sold with no photographs later uploaded to Rightmove's 'sold' houses has between 25 and a massive 48% of sales. That means they don't even hit any portals whatsoever.
Rightmove charge agents circa £1400-1500 a month. They don't care if you're a one man band or if you have 800 million in the bank. Don't want to pay? Sucks to be you. They have a horrific monopoly and their portal is absolutely shit; as is their customer service to both agents and buyers. Agents HATE having to use RM.
Onthemarket recently got a huge cash investment to re-invigorate the portal and agents are testing the market of leaving Rightmove to go back to ONM (who used to be the market leader); the last I can recall re: agent monthly fees, Zoopla was something like £400, OTM £200, and RM £1400.
I genuinely believe a good agent can sell a good house in a good, in demand area without having to use use Rightmove.
But, in this market, I would caveat it with 'fine, but the maximum contract I am prepared to sign with you is 4 weeks / fine: I hope you can sell my house, but because you are on not on Rightmove, I'm not prepared to sign a contract of any length with you, but I will agree fees in the event of a completion.' - So the contract is re: fees, not length of time.
If the agent balks at the 4 week contract stipulation, you know they are bluffing.
Have some faith, go for it, let us know if it works out for you.
*Mostly North Yorkshire, the 48% was a very popular village in Scotland - local knowledge, word of mouth and waiting lists of customers with specific requirements counts, it seems