In many professional situations, counteroffers only lead to bigger problems down the road. A counteroffer is usually a stall tactic for your manager to begin the search process to replace your position at a cheaper price. Everyone is dispensable and many times a company will do this on their schedule and terms after they have made you an attractive counteroffer to avoid any disruptions to the business.
Statistics show that 80% to 90% of those who accept counter offers quit within six months or are terminated within one year. That means that the promises your current employer committed to keep you to stay when you were resigning did not materialize. Many times, a company will make statements or promises out of desperation so as not to lose a valuable employee. They have no intention or motivation to make the drastic changes you are requesting. You have to ask yourself, why would a company change an entire corporate culture or a workforce because of one unhappy employee? The harsh reality is that there just isn't any incentive and it costs too much money.
Last but not least, your new employer has already made arrangements for your on boarding which includes training, company announcements and in some cases, dismissing the person in the current role who you may be replacing. It would be extremely unprofessional to go through the entire interview, offer and background process only to inform your new employer you are staying in your current role because your company extended a counteroffer. A company's motive for a counteroffer is usually to protect itself and the stability of the group. Many job seekers find themselves back at square one a year later; frustrated at accepting a counteroffer and even more frustrated in wasting the time of the new employer and missing out on a fantastic opportunity.