The new HPV vaccine protects against seven strains that are found in ∼90% of cervical cancers worldwide and against two strains implicated in more than 90% of anogenital warts. Given that, it is quite possible that for new generations coming through (who are vaccinated as children) population wide regular cervical screening will no longer be cost effective. Many developed countries are moving to fewer screens per lifetime at longer intervals (e.g. Australia moving to 5-yearly screening).
Unfortunately primary HPV screening with no cytology for negative results does mean that some women with HPV unrelated cervical cancer would be missed. However some women were missed under the old screening programme and HPV primary screening has been shown to be more effective at finding cases.
Younger generations who have been vaccinated before becoming sexually active should continue to attend screening as their vaccination does not protect against all strains.
Older generations and anyone unvaccinated should also attend as they may have HPV. Even if you have not been sexually active for some time or have been in a committed relationship for years you should still be tested again as HPV can lay dormant for years (or unfortunately a partner can be unfaithful).
I would not discourage anyone from screening, however if cervical screens make you extremely uncomfortable and your area has moved to HPV primary screening there is a case to be made for home testing yourself if you would prefer that.
Just to be clear I am not a health professional - and I am very open to being corrected by any!
Some free to read sources for my claims:
Effectiveness modelling and economic evaluationin the Australian setting. Note that "current practice" in 2013 was two-yearly testing.
[[https://onlinelibrary.wiley.com/doi/full/10.1002/ijc.30392
Will cervical screening remain cost‐effective in women offered the next generation nonavalent HPV vaccine?]]